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Deck 7: Probability

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Question
The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Find the height of the triangle that describes the probability density function. The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Find the height of the triangle that describes the probability density function. <div style=padding-top: 35px>
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Question
A density function for the age of people enrolled in a class is given in the following figure.
A. Find the value of c.
B. What percent of the class is over 20 years old? Round to the nearest whole percent. A density function for the age of people enrolled in a class is given in the following figure. A. Find the value of c. B. What percent of the class is over 20 years old? Round to the nearest whole percent. <div style=padding-top: 35px>
Question
The distribution of heights, x, in meters, of a group of shrubs is represented by the density function The distribution of heights, x, in meters, of a group of shrubs is represented by the density function (no shrubs are higher than 1.5 meters). Calculate the percentage of shrubs which are between 1 and 1.5 meter(s) high. <div style=padding-top: 35px> (no shrubs are higher than 1.5 meters). Calculate the percentage of shrubs which are between 1 and 1.5 meter(s) high. The distribution of heights, x, in meters, of a group of shrubs is represented by the density function (no shrubs are higher than 1.5 meters). Calculate the percentage of shrubs which are between 1 and 1.5 meter(s) high. <div style=padding-top: 35px>
Question
The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway. What percent of the cars drove less than 60 mph? <strong>The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway. What percent of the cars drove less than 60 mph? </strong> A)5% B)15% C)25% D)35% <div style=padding-top: 35px>

A)5%
B)15%
C)25%
D)35%
Question
Which of the following could possibly be density functions? Select all that apply.

A) <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px>
B) <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px>
C) <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px>
Question
The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway.Which were cars more likely to be driving? <strong>The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway.Which were cars more likely to be driving? </strong> A)Between 55 and 65 mph B)Between 70 and 80 mph <div style=padding-top: 35px>

A)Between 55 and 65 mph
B)Between 70 and 80 mph
Question
Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. <strong>Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. In terms of b (see the graph), find the fraction of the population that is between 60 and 100 years old.</strong> A)60b B)20b C)40b D)80b <div style=padding-top: 35px> In terms of b (see the graph), find the fraction of the population that is between 60 and 100 years old.

A)60b
B)20b
C)40b
D)80b
Question
An aptitude test is given to a group of students. Scores can range from 0 to 50. Does the cumulative distribution function in the second graph correspond to the density function in the first graph? Answer "yes" or "no" An aptitude test is given to a group of students. Scores can range from 0 to 50. Does the cumulative distribution function in the second graph correspond to the density function in the first graph? Answer yes or no <div style=padding-top: 35px> An aptitude test is given to a group of students. Scores can range from 0 to 50. Does the cumulative distribution function in the second graph correspond to the density function in the first graph? Answer yes or no <div style=padding-top: 35px>
Question
A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: Find the value of the height h of the triangular probability density function.<div style=padding-top: 35px> Find the value of the height h of the triangular probability density function.
Question
The following figure gives the density function for the number of hours students spent studying for a calculus exam. What is the largest amount of time a student spent studying? <strong>The following figure gives the density function for the number of hours students spent studying for a calculus exam. What is the largest amount of time a student spent studying? </strong> A)1 hour B)3 hours C)4 hours D)6 hours E)8 hours <div style=padding-top: 35px>

A)1 hour
B)3 hours
C)4 hours
D)6 hours
E)8 hours
Question
Suppose <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D) <div style=padding-top: 35px> is a density function for a certain distribution and <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D) <div style=padding-top: 35px> is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.

A) <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D) <div style=padding-top: 35px>
B) <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D) <div style=padding-top: 35px>
C) <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D) <div style=padding-top: 35px>
D) <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D) <div style=padding-top: 35px>
Question
The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. What is the probability that the circuit board will cost less than $2 thousand to produce? The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. What is the probability that the circuit board will cost less than $2 thousand to produce? <div style=padding-top: 35px>
Question
A density function for the daily calorie intake of a certain species is given in the following figure.
A. Find the value of c.
B. What percent have daily calorie intake between 30 and 40? A density function for the daily calorie intake of a certain species is given in the following figure. A. Find the value of c. B. What percent have daily calorie intake between 30 and 40? <div style=padding-top: 35px>
Question
A density function for the lifetime of a certain type of frog is shown in the following figure. Which is the frog's lifetime more likely to be between? <strong>A density function for the lifetime of a certain type of frog is shown in the following figure. Which is the frog's lifetime more likely to be between? </strong> A)7 and 8 months B)10 and 11 months C)13 and 14 months <div style=padding-top: 35px>

A)7 and 8 months
B)10 and 11 months
C)13 and 14 months
Question
The cumulative distribution function in the second graph corresponds to the density function in the first graph. The cumulative distribution function in the second graph corresponds to the density function in the first graph. <div style=padding-top: 35px> The cumulative distribution function in the second graph corresponds to the density function in the first graph. <div style=padding-top: 35px>
Question
A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: What percent of the students would you expect to score below 25 points on the exam?<div style=padding-top: 35px> What percent of the students would you expect to score below 25 points on the exam?
Question
Suppose <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) <div style=padding-top: 35px> is the cumulative distribution function for sizes of graduating classes among a group of high schools and <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) <div style=padding-top: 35px> . Which of the following are possible statements about <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) <div style=padding-top: 35px> ?

A) <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) <div style=padding-top: 35px>
B) <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) <div style=padding-top: 35px>
C) <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) <div style=padding-top: 35px>
Question
Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. According to this simplified model of the distribution of people's ages in the United States, what percentage of the population is between 0 and 100 years old?<div style=padding-top: 35px> According to this simplified model of the distribution of people's ages in the United States, what percentage of the population is between 0 and 100 years old?
Question
The following figure gives the density function for the number of hours students spent studying for a calculus exam. Did a greater number of students study more than 2 hours or less than 2 hours? Answer "more" or "less". The following figure gives the density function for the number of hours students spent studying for a calculus exam. Did a greater number of students study more than 2 hours or less than 2 hours? Answer more or less. <div style=padding-top: 35px>
Question
The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D) <div style=padding-top: 35px>

A) <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D) <div style=padding-top: 35px>
B) <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D) <div style=padding-top: 35px>
C) <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D) <div style=padding-top: 35px>
D) <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D) <div style=padding-top: 35px>
Question
The probability of waiting no more than m minutes for a taxi on a certain street corner is
P( The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the mean waiting time.<div style=padding-top: 35px> ) = The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the mean waiting time.<div style=padding-top: 35px> .
Find the mean waiting time.
Question
The probability of waiting no more than m minutes for a taxi on a certain street corner is
P( The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the probability of waiting more than 10 minutes. Round to 3 decimal places.<div style=padding-top: 35px> ) = The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the probability of waiting more than 10 minutes. Round to 3 decimal places.<div style=padding-top: 35px> .
Find the probability of waiting more than 10 minutes. Round to 3 decimal places.
Question
A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by <strong>A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by . If you select a banana leaf at random, what is the probability that it emerged in the first 4 months?</strong> A)0.69 B)0.23 C)0.87 D)0.55 <div style=padding-top: 35px> . If you select a banana leaf at random, what is the probability that it emerged in the first 4 months?

A)0.69
B)0.23
C)0.87
D)0.55
Question
The following figure shows a density function and the corresponding distribution function. Which curve represents the cumulative distribution function? The following figure shows a density function and the corresponding distribution function. Which curve represents the cumulative distribution function? <div style=padding-top: 35px>
Question
The density function for the height of trees in a forest is given by The density function for the height of trees in a forest is given by , where x is height in meters and the tallest tree is 10 meters. Find the cumulative distribution function, , for this density function.<div style=padding-top: 35px> , where x is height in meters and the tallest tree is 10 meters. Find the cumulative distribution function, The density function for the height of trees in a forest is given by , where x is height in meters and the tallest tree is 10 meters. Find the cumulative distribution function, , for this density function.<div style=padding-top: 35px> , for this density function.
Question
The graph of a probability density function is given. Sketch a graph of the cumulative distribution function. The graph of a probability density function is given. Sketch a graph of the cumulative distribution function. <div style=padding-top: 35px>
Question
Let Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What fraction of the students took between 12 and 18 credits? <div style=padding-top: 35px> be the cumulative distribution function for the number of credits taken by students at a community college. Some values of Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What fraction of the students took between 12 and 18 credits? <div style=padding-top: 35px> are shown in the following table. What fraction of the students took between 12 and 18 credits? Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What fraction of the students took between 12 and 18 credits? <div style=padding-top: 35px>
Question
The following figure shows a density function and the corresponding distribution function. The drawing is not to scale. What is a reasonable estimate for b? <strong>The following figure shows a density function and the corresponding distribution function. The drawing is not to scale. What is a reasonable estimate for b? </strong> A)1 B)2 C)3 D)4 E)cannot be determined <div style=padding-top: 35px>

A)1
B)2
C)3
D)4
E)cannot be determined
Question
The life expectancy of a bug can be approximated by the density function The life expectancy of a bug can be approximated by the density function , where t is time in days. Find the probability that a bug lives between 3 and 5 days. Round to 2 decimal places.<div style=padding-top: 35px> , where t is time in days. Find the probability that a bug lives between 3 and 5 days. Round to 2 decimal places.
Question
The density function for the height of trees in a forest is given by The density function for the height of trees in a forest is given by , where x is height in meters and the tallest tree is 10 meters. Find the probability, to 3 decimal places, that a tree is between 5 and 8 meters tall.<div style=padding-top: 35px> , where x is height in meters and the tallest tree is 10 meters. Find the probability, to 3 decimal places, that a tree is between 5 and 8 meters tall.
Question
The following figure shows a density function and the corresponding distribution function. What is the value of a? The following figure shows a density function and the corresponding distribution function. What is the value of a? <div style=padding-top: 35px>
Question
The probability of waiting no more than m minutes for a taxi on a certain street corner is
P( The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the median waiting time to 3 decimal places.<div style=padding-top: 35px> ) = The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the median waiting time to 3 decimal places.<div style=padding-top: 35px> .
Find the median waiting time to 3 decimal places.
Question
Which of the following could possibly be cumulative distribution functions? Select all that apply.

A) <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px>
B) <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px>
C) <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for <div style=padding-top: 35px>
Question
Let p(t) be a probability density which is defined for 0 ≤\le t ≤\le 1. Could the following be the cumulative distribution function for p? Let p(t) be a probability density which is defined for 0 \le t \le 1. Could the following be the cumulative distribution function for p? <div style=padding-top: 35px>
Question
The heights, in inches, of flowers in a garden have the density function shown in the following figure. How many inches tall is the tallest flower? The heights, in inches, of flowers in a garden have the density function shown in the following figure. How many inches tall is the tallest flower? <div style=padding-top: 35px>
Question
Let Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What was the median number of credit hours taken by the students? <div style=padding-top: 35px> be the cumulative distribution function for the number of credits taken by students at a community college. Some values of Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What was the median number of credit hours taken by the students? <div style=padding-top: 35px> are shown in the following table. What was the median number of credit hours taken by the students? Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What was the median number of credit hours taken by the students? <div style=padding-top: 35px>
Question
Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk?
I. Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk? I. II. III. <div style=padding-top: 35px> II. Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk? I. II. III. <div style=padding-top: 35px> III. Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk? I. II. III. <div style=padding-top: 35px>
Question
The cumulative distribution function for the time to complete a step on an assembly line is given in the following table. What percent of the steps take from 0 to 14 minutes to complete? The cumulative distribution function for the time to complete a step on an assembly line is given in the following table. What percent of the steps take from 0 to 14 minutes to complete? <div style=padding-top: 35px>
Question
The heights, in inches, of flowers in a garden have the density function shown in the following figure. The median height is <strong>The heights, in inches, of flowers in a garden have the density function shown in the following figure. The median height is </strong> A)less than 20 inches. B)equal to 20 inches. C)greater than 20 inches. <div style=padding-top: 35px>

A)less than 20 inches.
B)equal to 20 inches.
C)greater than 20 inches.
Question
The life expectancy of a bug can be approximated by the density function The life expectancy of a bug can be approximated by the density function , where t is time in days. Find the cumulative distribution function, , associated with this density function.<div style=padding-top: 35px> , where t is time in days. Find the cumulative distribution function, The life expectancy of a bug can be approximated by the density function , where t is time in days. Find the cumulative distribution function, , associated with this density function.<div style=padding-top: 35px> , associated with this density function.
Question
The density function for lunch time taken by a group of office workers is given by The density function for lunch time taken by a group of office workers is given by . The maximum allowable lunch time is 1 hour, so we have . A. Find the median number of hours taken, to 2 decimal places. B. Find the mean number of hours taken, to 2 decimal places.<div style=padding-top: 35px> . The maximum allowable lunch time is 1 hour, so we have The density function for lunch time taken by a group of office workers is given by . The maximum allowable lunch time is 1 hour, so we have . A. Find the median number of hours taken, to 2 decimal places. B. Find the mean number of hours taken, to 2 decimal places.<div style=padding-top: 35px> .
A. Find the median number of hours taken, to 2 decimal places.
B. Find the mean number of hours taken, to 2 decimal places.
Question
The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?

A) <strong>The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?</strong> A) B) C) D) <div style=padding-top: 35px>
B) <strong>The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?</strong> A) B) C) D) <div style=padding-top: 35px>
C) <strong>The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?</strong> A) B) C) D) <div style=padding-top: 35px>
D) <strong>The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?</strong> A) B) C) D) <div style=padding-top: 35px>
Question
According to data from 2007, the height of five-year-old girls is normally distributed with a mean of 42 inches and a standard deviation of 1.5 inches. Use your calculator or computer to find the percentage of 5-year-old girls between 43 and 44 inches.

A)25
B)22
C)12
D)83
Question
A density function is given by <strong>A density function is given by for . Estimate the median of the distribution.</strong> A)1.16 B)1.54 C)1.02 D)1.78 <div style=padding-top: 35px> for <strong>A density function is given by for . Estimate the median of the distribution.</strong> A)1.16 B)1.54 C)1.02 D)1.78 <div style=padding-top: 35px> . Estimate the median of the distribution.

A)1.16
B)1.54
C)1.02
D)1.78
Question
The density function for the shelf life, in days, of a product in a grocery store is shown in the graph. <strong>The density function for the shelf life, in days, of a product in a grocery store is shown in the graph. Estimate the median shelf life of the product.</strong> A)2.25 days B)3.25 days C)4.25 days D)5.25 days <div style=padding-top: 35px> Estimate the median shelf life of the product.

A)2.25 days
B)3.25 days
C)4.25 days
D)5.25 days
Question
In the following probability density function, is the mean smaller or greater than the median? In the following probability density function, is the mean smaller or greater than the median? <div style=padding-top: 35px>
Question
Suppose scores from a standardized test measure from 0 to 100. If most scores were in the middle (with few extremely high or low scores), pick the graph that best represents the cumulative distribution function. Suppose scores from a standardized test measure from 0 to 100. If most scores were in the middle (with few extremely high or low scores), pick the graph that best represents the cumulative distribution function. <div style=padding-top: 35px>
Question
Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?

A) <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for <div style=padding-top: 35px>
B) <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for <div style=padding-top: 35px>
C) <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for <div style=padding-top: 35px> for <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for <div style=padding-top: 35px>
Question
According to data from 2007, the height of five-year-old girls is normally distributed with a mean of 42 inches and a standard deviation of 1.5 inches. Write the formula for the density function for height of five-year-old girls.
Question
The following figure shows the distribution of the number of hours of television viewed per day by a group of children. Estimate the percent of the children who watched less than 3 hours per day. <strong>The following figure shows the distribution of the number of hours of television viewed per day by a group of children. Estimate the percent of the children who watched less than 3 hours per day. </strong> A)65% B)95% C)50% D)80% <div style=padding-top: 35px>

A)65%
B)95%
C)50%
D)80%
Question
A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by <strong>A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by . Use a calculator or computer to find the median time of emergence.</strong> A)2.7 months B)2.4 months C)3.3 months D)4.0 months <div style=padding-top: 35px> . Use a calculator or computer to find the median time of emergence.

A)2.7 months
B)2.4 months
C)3.3 months
D)4.0 months
Question
The final exam scores for a calculus course were approximately normally distributed with mean The final exam scores for a calculus course were approximately normally distributed with mean and standard deviation . The maximum possible score was 100. What is the probability that a randomly selected student received an A grade (90 or higher)? Round to 3 decimal places.<div style=padding-top: 35px> and standard deviation The final exam scores for a calculus course were approximately normally distributed with mean and standard deviation . The maximum possible score was 100. What is the probability that a randomly selected student received an A grade (90 or higher)? Round to 3 decimal places.<div style=padding-top: 35px> . The maximum possible score was 100. What is the probability that a randomly selected student received an A grade (90 or higher)? Round to 3 decimal places.
Question
The annual rainfall for a desert city is approximately normally distributed with mean 7 and standard deviation 1. What is the probability that the annual rainfall will be between 6 and 8 inches? Round to 2 decimal places.
Question
The lifespan of a bug is approximately normally distributed with mean The lifespan of a bug is approximately normally distributed with mean days and standard deviation days. Assume a maximum possible lifespan of 3 weeks. What is the probability of a randomly selected bug living less than a week? Round to 2 decimal places.<div style=padding-top: 35px> days and standard deviation The lifespan of a bug is approximately normally distributed with mean days and standard deviation days. Assume a maximum possible lifespan of 3 weeks. What is the probability of a randomly selected bug living less than a week? Round to 2 decimal places.<div style=padding-top: 35px> days. Assume a maximum possible lifespan of 3 weeks. What is the probability of a randomly selected bug living less than a week? Round to 2 decimal places.
Question
Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community?
I. Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community? I. II. III. <div style=padding-top: 35px> II. Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community? I. II. III. <div style=padding-top: 35px> III. Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community? I. II. III. <div style=padding-top: 35px>
Question
Using the following figure, calculate the value of c if p is a density function. Using the following figure, calculate the value of c if p is a density function. <div style=padding-top: 35px>
Question
The probability of a plant surviving t days without water is given by The probability of a plant surviving t days without water is given by for some constant c. If the probability of the plant surviving 6 days without water is 0.8, what is c? Round to 2 decimal places.<div style=padding-top: 35px> for some constant c. If the probability of the plant surviving 6 days without water is 0.8, what is c? Round to 2 decimal places.
Question
The density function for the time to complete a certain task is approximately equal to The density function for the time to complete a certain task is approximately equal to , where t is time in minutes and . A. Find the median number of minutes taken, to 2 decimal places. B. Find the mean number of minutes taken, to 2 decimal places.<div style=padding-top: 35px> , where t is time in minutes and The density function for the time to complete a certain task is approximately equal to , where t is time in minutes and . A. Find the median number of minutes taken, to 2 decimal places. B. Find the mean number of minutes taken, to 2 decimal places.<div style=padding-top: 35px> .
A. Find the median number of minutes taken, to 2 decimal places.
B. Find the mean number of minutes taken, to 2 decimal places.
Question
A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: Do the mean and the median both describe the same point on this probability density function?<div style=padding-top: 35px> Do the mean and the median both describe the same point on this probability density function?
Question
Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. Find the median age of the United States population.<div style=padding-top: 35px> Find the median age of the United States population.
Question
Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?

A) <strong>Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?</strong> A) B) C) D) <div style=padding-top: 35px>
B) <strong>Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?</strong> A) B) C) D) <div style=padding-top: 35px>
C) <strong>Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?</strong> A) B) C) D) <div style=padding-top: 35px>
D) <strong>Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?</strong> A) B) C) D) <div style=padding-top: 35px>
Question
Let Let be the density function for call-back time by an answering service with t = time in minutes and . Find the mean, in minutes, to 2 decimal places.<div style=padding-top: 35px> be the density function for call-back time by an answering service with t = time in minutes and Let be the density function for call-back time by an answering service with t = time in minutes and . Find the mean, in minutes, to 2 decimal places.<div style=padding-top: 35px> . Find the mean, in minutes, to 2 decimal places.
Question
The number of hours of sleep per night averaged by a group of students is approximately normally distributed with mean The number of hours of sleep per night averaged by a group of students is approximately normally distributed with mean and standard deviation . What is the probability that a student selected at random had more than 7.5 hours of sleep? Round to 2 decimal places.<div style=padding-top: 35px> and standard deviation The number of hours of sleep per night averaged by a group of students is approximately normally distributed with mean and standard deviation . What is the probability that a student selected at random had more than 7.5 hours of sleep? Round to 2 decimal places.<div style=padding-top: 35px> . What is the probability that a student selected at random had more than 7.5 hours of sleep? Round to 2 decimal places.
Question
The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function and the corresponding cumulative distribution function , where t is time in minutes. Express in terms of .<div style=padding-top: 35px> and the corresponding cumulative distribution function The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function and the corresponding cumulative distribution function , where t is time in minutes. Express in terms of .<div style=padding-top: 35px> , where t is time in minutes. Express The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function and the corresponding cumulative distribution function , where t is time in minutes. Express in terms of .<div style=padding-top: 35px> in terms of The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function and the corresponding cumulative distribution function , where t is time in minutes. Express in terms of .<div style=padding-top: 35px> .
Question
The speed of cars on a freeway are approximately normally distributed with mean The speed of cars on a freeway are approximately normally distributed with mean mph and standard deviation mph. Assume a maximum speed of 100 mph. What percent of cars are going between 65 and 70 mph? Round to the nearest percent.<div style=padding-top: 35px> mph and standard deviation The speed of cars on a freeway are approximately normally distributed with mean mph and standard deviation mph. Assume a maximum speed of 100 mph. What percent of cars are going between 65 and 70 mph? Round to the nearest percent.<div style=padding-top: 35px> mph. Assume a maximum speed of 100 mph. What percent of cars are going between 65 and 70 mph? Round to the nearest percent.
Question
The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. Which figure is the cumulative distribution function?
I. The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. Which figure is the cumulative distribution function? I. II. <div style=padding-top: 35px> II. The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. Which figure is the cumulative distribution function? I. II. <div style=padding-top: 35px>
Question
The speed of cars on a freeway are approximately normally distributed with mean The speed of cars on a freeway are approximately normally distributed with mean mph and standard deviation mph. Assume a maximum speed of 100 mph. If speeding tickets are given to cars traveling faster than 82 mph, what is the probability that a randomly selected car is going fast enough to get a ticket? Round to 2 decimal places.<div style=padding-top: 35px> mph and standard deviation The speed of cars on a freeway are approximately normally distributed with mean mph and standard deviation mph. Assume a maximum speed of 100 mph. If speeding tickets are given to cars traveling faster than 82 mph, what is the probability that a randomly selected car is going fast enough to get a ticket? Round to 2 decimal places.<div style=padding-top: 35px> mph. Assume a maximum speed of 100 mph. If speeding tickets are given to cars traveling faster than 82 mph, what is the probability that a randomly selected car is going fast enough to get a ticket? Round to 2 decimal places.
Question
The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. About what percent of the people in the school are adults? I. <strong>The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. About what percent of the people in the school are adults? I. II. </strong> A)20% B)40% C)60% D)80% <div style=padding-top: 35px> II. <strong>The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. About what percent of the people in the school are adults? I. II. </strong> A)20% B)40% C)60% D)80% <div style=padding-top: 35px>

A)20%
B)40%
C)60%
D)80%
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Deck 7: Probability
1
The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Find the height of the triangle that describes the probability density function. The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Find the height of the triangle that describes the probability density function.
0.25
2
A density function for the age of people enrolled in a class is given in the following figure.
A. Find the value of c.
B. What percent of the class is over 20 years old? Round to the nearest whole percent. A density function for the age of people enrolled in a class is given in the following figure. A. Find the value of c. B. What percent of the class is over 20 years old? Round to the nearest whole percent.
A. 1/15
B. 83%
3
The distribution of heights, x, in meters, of a group of shrubs is represented by the density function The distribution of heights, x, in meters, of a group of shrubs is represented by the density function (no shrubs are higher than 1.5 meters). Calculate the percentage of shrubs which are between 1 and 1.5 meter(s) high. (no shrubs are higher than 1.5 meters). Calculate the percentage of shrubs which are between 1 and 1.5 meter(s) high. The distribution of heights, x, in meters, of a group of shrubs is represented by the density function (no shrubs are higher than 1.5 meters). Calculate the percentage of shrubs which are between 1 and 1.5 meter(s) high.
40%
4
The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway. What percent of the cars drove less than 60 mph? <strong>The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway. What percent of the cars drove less than 60 mph? </strong> A)5% B)15% C)25% D)35%

A)5%
B)15%
C)25%
D)35%
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5
Which of the following could possibly be density functions? Select all that apply.

A) <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for for <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for
B) <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for for <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for
C) <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for for <strong>Which of the following could possibly be density functions? Select all that apply.</strong> A) for B) for C) for
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6
The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway.Which were cars more likely to be driving? <strong>The following figure gives the density function for the velocities of cars passing a checkpoint on a freeway.Which were cars more likely to be driving? </strong> A)Between 55 and 65 mph B)Between 70 and 80 mph

A)Between 55 and 65 mph
B)Between 70 and 80 mph
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7
Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. <strong>Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. In terms of b (see the graph), find the fraction of the population that is between 60 and 100 years old.</strong> A)60b B)20b C)40b D)80b In terms of b (see the graph), find the fraction of the population that is between 60 and 100 years old.

A)60b
B)20b
C)40b
D)80b
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8
An aptitude test is given to a group of students. Scores can range from 0 to 50. Does the cumulative distribution function in the second graph correspond to the density function in the first graph? Answer "yes" or "no" An aptitude test is given to a group of students. Scores can range from 0 to 50. Does the cumulative distribution function in the second graph correspond to the density function in the first graph? Answer yes or no An aptitude test is given to a group of students. Scores can range from 0 to 50. Does the cumulative distribution function in the second graph correspond to the density function in the first graph? Answer yes or no
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9
A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: Find the value of the height h of the triangular probability density function. Find the value of the height h of the triangular probability density function.
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10
The following figure gives the density function for the number of hours students spent studying for a calculus exam. What is the largest amount of time a student spent studying? <strong>The following figure gives the density function for the number of hours students spent studying for a calculus exam. What is the largest amount of time a student spent studying? </strong> A)1 hour B)3 hours C)4 hours D)6 hours E)8 hours

A)1 hour
B)3 hours
C)4 hours
D)6 hours
E)8 hours
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11
Suppose <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D) is a density function for a certain distribution and <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D) is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.

A) <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D)
B) <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D)
C) <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D)
D) <strong>Suppose is a density function for a certain distribution and is the cumulative distribution function for the same distribution. Which of the following gives the fraction of the distribution between x = 7 and x = 16? Select all that apply.</strong> A) B) C) D)
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12
The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. What is the probability that the circuit board will cost less than $2 thousand to produce? The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. What is the probability that the circuit board will cost less than $2 thousand to produce?
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13
A density function for the daily calorie intake of a certain species is given in the following figure.
A. Find the value of c.
B. What percent have daily calorie intake between 30 and 40? A density function for the daily calorie intake of a certain species is given in the following figure. A. Find the value of c. B. What percent have daily calorie intake between 30 and 40?
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14
A density function for the lifetime of a certain type of frog is shown in the following figure. Which is the frog's lifetime more likely to be between? <strong>A density function for the lifetime of a certain type of frog is shown in the following figure. Which is the frog's lifetime more likely to be between? </strong> A)7 and 8 months B)10 and 11 months C)13 and 14 months

A)7 and 8 months
B)10 and 11 months
C)13 and 14 months
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15
The cumulative distribution function in the second graph corresponds to the density function in the first graph. The cumulative distribution function in the second graph corresponds to the density function in the first graph. The cumulative distribution function in the second graph corresponds to the density function in the first graph.
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16
A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: What percent of the students would you expect to score below 25 points on the exam? What percent of the students would you expect to score below 25 points on the exam?
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17
Suppose <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) is the cumulative distribution function for sizes of graduating classes among a group of high schools and <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) . Which of the following are possible statements about <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C) ?

A) <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C)
B) <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C)
C) <strong>Suppose is the cumulative distribution function for sizes of graduating classes among a group of high schools and . Which of the following are possible statements about ?</strong> A) B) C)
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18
Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. According to this simplified model of the distribution of people's ages in the United States, what percentage of the population is between 0 and 100 years old? According to this simplified model of the distribution of people's ages in the United States, what percentage of the population is between 0 and 100 years old?
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19
The following figure gives the density function for the number of hours students spent studying for a calculus exam. Did a greater number of students study more than 2 hours or less than 2 hours? Answer "more" or "less". The following figure gives the density function for the number of hours students spent studying for a calculus exam. Did a greater number of students study more than 2 hours or less than 2 hours? Answer more or less.
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20
The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D)

A) <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D)
B) <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D)
C) <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D)
D) <strong>The density function f(x) shown below describes the probability that a computer circuit board will cost a manufacturer more than a certain number of dollars to produce. In this case, the cost of the circuit board, x, is measured in thousands of dollars. Which of the following definite integrals give the probability that the circuit board will cost between $2 thousand and some amount $b thousand? Assume that b is between 2 and 10. </strong> A) B) C) D)
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21
The probability of waiting no more than m minutes for a taxi on a certain street corner is
P( The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the mean waiting time. ) = The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the mean waiting time. .
Find the mean waiting time.
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22
The probability of waiting no more than m minutes for a taxi on a certain street corner is
P( The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the probability of waiting more than 10 minutes. Round to 3 decimal places. ) = The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the probability of waiting more than 10 minutes. Round to 3 decimal places. .
Find the probability of waiting more than 10 minutes. Round to 3 decimal places.
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23
A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by <strong>A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by . If you select a banana leaf at random, what is the probability that it emerged in the first 4 months?</strong> A)0.69 B)0.23 C)0.87 D)0.55 . If you select a banana leaf at random, what is the probability that it emerged in the first 4 months?

A)0.69
B)0.23
C)0.87
D)0.55
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24
The following figure shows a density function and the corresponding distribution function. Which curve represents the cumulative distribution function? The following figure shows a density function and the corresponding distribution function. Which curve represents the cumulative distribution function?
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25
The density function for the height of trees in a forest is given by The density function for the height of trees in a forest is given by , where x is height in meters and the tallest tree is 10 meters. Find the cumulative distribution function, , for this density function. , where x is height in meters and the tallest tree is 10 meters. Find the cumulative distribution function, The density function for the height of trees in a forest is given by , where x is height in meters and the tallest tree is 10 meters. Find the cumulative distribution function, , for this density function. , for this density function.
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26
The graph of a probability density function is given. Sketch a graph of the cumulative distribution function. The graph of a probability density function is given. Sketch a graph of the cumulative distribution function.
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27
Let Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What fraction of the students took between 12 and 18 credits? be the cumulative distribution function for the number of credits taken by students at a community college. Some values of Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What fraction of the students took between 12 and 18 credits? are shown in the following table. What fraction of the students took between 12 and 18 credits? Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What fraction of the students took between 12 and 18 credits?
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28
The following figure shows a density function and the corresponding distribution function. The drawing is not to scale. What is a reasonable estimate for b? <strong>The following figure shows a density function and the corresponding distribution function. The drawing is not to scale. What is a reasonable estimate for b? </strong> A)1 B)2 C)3 D)4 E)cannot be determined

A)1
B)2
C)3
D)4
E)cannot be determined
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29
The life expectancy of a bug can be approximated by the density function The life expectancy of a bug can be approximated by the density function , where t is time in days. Find the probability that a bug lives between 3 and 5 days. Round to 2 decimal places. , where t is time in days. Find the probability that a bug lives between 3 and 5 days. Round to 2 decimal places.
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30
The density function for the height of trees in a forest is given by The density function for the height of trees in a forest is given by , where x is height in meters and the tallest tree is 10 meters. Find the probability, to 3 decimal places, that a tree is between 5 and 8 meters tall. , where x is height in meters and the tallest tree is 10 meters. Find the probability, to 3 decimal places, that a tree is between 5 and 8 meters tall.
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31
The following figure shows a density function and the corresponding distribution function. What is the value of a? The following figure shows a density function and the corresponding distribution function. What is the value of a?
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32
The probability of waiting no more than m minutes for a taxi on a certain street corner is
P( The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the median waiting time to 3 decimal places. ) = The probability of waiting no more than m minutes for a taxi on a certain street corner is P( ) = . Find the median waiting time to 3 decimal places. .
Find the median waiting time to 3 decimal places.
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33
Which of the following could possibly be cumulative distribution functions? Select all that apply.

A) <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for for <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for
B) <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for for <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for
C) <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for for <strong>Which of the following could possibly be cumulative distribution functions? Select all that apply.</strong> A) for B) for C) for
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34
Let p(t) be a probability density which is defined for 0 ≤\le t ≤\le 1. Could the following be the cumulative distribution function for p? Let p(t) be a probability density which is defined for 0 \le t \le 1. Could the following be the cumulative distribution function for p?
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35
The heights, in inches, of flowers in a garden have the density function shown in the following figure. How many inches tall is the tallest flower? The heights, in inches, of flowers in a garden have the density function shown in the following figure. How many inches tall is the tallest flower?
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36
Let Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What was the median number of credit hours taken by the students? be the cumulative distribution function for the number of credits taken by students at a community college. Some values of Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What was the median number of credit hours taken by the students? are shown in the following table. What was the median number of credit hours taken by the students? Let be the cumulative distribution function for the number of credits taken by students at a community college. Some values of are shown in the following table. What was the median number of credit hours taken by the students?
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37
Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk?
I. Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk? I. II. III. II. Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk? I. II. III. III. Which of the following cumulative distribution graphs would most likely represent the total annual sales of milk? I. II. III.
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38
The cumulative distribution function for the time to complete a step on an assembly line is given in the following table. What percent of the steps take from 0 to 14 minutes to complete? The cumulative distribution function for the time to complete a step on an assembly line is given in the following table. What percent of the steps take from 0 to 14 minutes to complete?
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39
The heights, in inches, of flowers in a garden have the density function shown in the following figure. The median height is <strong>The heights, in inches, of flowers in a garden have the density function shown in the following figure. The median height is </strong> A)less than 20 inches. B)equal to 20 inches. C)greater than 20 inches.

A)less than 20 inches.
B)equal to 20 inches.
C)greater than 20 inches.
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40
The life expectancy of a bug can be approximated by the density function The life expectancy of a bug can be approximated by the density function , where t is time in days. Find the cumulative distribution function, , associated with this density function. , where t is time in days. Find the cumulative distribution function, The life expectancy of a bug can be approximated by the density function , where t is time in days. Find the cumulative distribution function, , associated with this density function. , associated with this density function.
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41
The density function for lunch time taken by a group of office workers is given by The density function for lunch time taken by a group of office workers is given by . The maximum allowable lunch time is 1 hour, so we have . A. Find the median number of hours taken, to 2 decimal places. B. Find the mean number of hours taken, to 2 decimal places. . The maximum allowable lunch time is 1 hour, so we have The density function for lunch time taken by a group of office workers is given by . The maximum allowable lunch time is 1 hour, so we have . A. Find the median number of hours taken, to 2 decimal places. B. Find the mean number of hours taken, to 2 decimal places. .
A. Find the median number of hours taken, to 2 decimal places.
B. Find the mean number of hours taken, to 2 decimal places.
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42
The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?

A) <strong>The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?</strong> A) B) C) D)
B) <strong>The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?</strong> A) B) C) D)
C) <strong>The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?</strong> A) B) C) D)
D) <strong>The annual rainfall for a desert city is approximately normally distributed with mean 4 and standard deviation 1. Which of the following is the density function for annual rainfall?</strong> A) B) C) D)
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43
According to data from 2007, the height of five-year-old girls is normally distributed with a mean of 42 inches and a standard deviation of 1.5 inches. Use your calculator or computer to find the percentage of 5-year-old girls between 43 and 44 inches.

A)25
B)22
C)12
D)83
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44
A density function is given by <strong>A density function is given by for . Estimate the median of the distribution.</strong> A)1.16 B)1.54 C)1.02 D)1.78 for <strong>A density function is given by for . Estimate the median of the distribution.</strong> A)1.16 B)1.54 C)1.02 D)1.78 . Estimate the median of the distribution.

A)1.16
B)1.54
C)1.02
D)1.78
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45
The density function for the shelf life, in days, of a product in a grocery store is shown in the graph. <strong>The density function for the shelf life, in days, of a product in a grocery store is shown in the graph. Estimate the median shelf life of the product.</strong> A)2.25 days B)3.25 days C)4.25 days D)5.25 days Estimate the median shelf life of the product.

A)2.25 days
B)3.25 days
C)4.25 days
D)5.25 days
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46
In the following probability density function, is the mean smaller or greater than the median? In the following probability density function, is the mean smaller or greater than the median?
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47
Suppose scores from a standardized test measure from 0 to 100. If most scores were in the middle (with few extremely high or low scores), pick the graph that best represents the cumulative distribution function. Suppose scores from a standardized test measure from 0 to 100. If most scores were in the middle (with few extremely high or low scores), pick the graph that best represents the cumulative distribution function.
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48
Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?

A) <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for for <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for
B) <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for for <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for
C) <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for for <strong>Which of the following functions makes the most sense as a model for the probability density function representing a random value chosen between 0 and 1?</strong> A) for B) for C) for
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49
According to data from 2007, the height of five-year-old girls is normally distributed with a mean of 42 inches and a standard deviation of 1.5 inches. Write the formula for the density function for height of five-year-old girls.
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50
The following figure shows the distribution of the number of hours of television viewed per day by a group of children. Estimate the percent of the children who watched less than 3 hours per day. <strong>The following figure shows the distribution of the number of hours of television viewed per day by a group of children. Estimate the percent of the children who watched less than 3 hours per day. </strong> A)65% B)95% C)50% D)80%

A)65%
B)95%
C)50%
D)80%
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51
A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by <strong>A banana plant typically has about 40 leaves that emerge over a period of 238 days (8 months). Younger leaves emerge more rapidly than later leaves. If you randomly select a banana leaf, the probability density function for the month of emergence is given by . Use a calculator or computer to find the median time of emergence.</strong> A)2.7 months B)2.4 months C)3.3 months D)4.0 months . Use a calculator or computer to find the median time of emergence.

A)2.7 months
B)2.4 months
C)3.3 months
D)4.0 months
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52
The final exam scores for a calculus course were approximately normally distributed with mean The final exam scores for a calculus course were approximately normally distributed with mean and standard deviation . The maximum possible score was 100. What is the probability that a randomly selected student received an A grade (90 or higher)? Round to 3 decimal places. and standard deviation The final exam scores for a calculus course were approximately normally distributed with mean and standard deviation . The maximum possible score was 100. What is the probability that a randomly selected student received an A grade (90 or higher)? Round to 3 decimal places. . The maximum possible score was 100. What is the probability that a randomly selected student received an A grade (90 or higher)? Round to 3 decimal places.
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53
The annual rainfall for a desert city is approximately normally distributed with mean 7 and standard deviation 1. What is the probability that the annual rainfall will be between 6 and 8 inches? Round to 2 decimal places.
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54
The lifespan of a bug is approximately normally distributed with mean The lifespan of a bug is approximately normally distributed with mean days and standard deviation days. Assume a maximum possible lifespan of 3 weeks. What is the probability of a randomly selected bug living less than a week? Round to 2 decimal places. days and standard deviation The lifespan of a bug is approximately normally distributed with mean days and standard deviation days. Assume a maximum possible lifespan of 3 weeks. What is the probability of a randomly selected bug living less than a week? Round to 2 decimal places. days. Assume a maximum possible lifespan of 3 weeks. What is the probability of a randomly selected bug living less than a week? Round to 2 decimal places.
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55
Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community?
I. Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community? I. II. III. II. Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community? I. II. III. III. Each of the following density functions represents the heights of a group of people in a community. Which one most likely represents the heights of a group consisting of only the children in the community? I. II. III.
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56
Using the following figure, calculate the value of c if p is a density function. Using the following figure, calculate the value of c if p is a density function.
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57
The probability of a plant surviving t days without water is given by The probability of a plant surviving t days without water is given by for some constant c. If the probability of the plant surviving 6 days without water is 0.8, what is c? Round to 2 decimal places. for some constant c. If the probability of the plant surviving 6 days without water is 0.8, what is c? Round to 2 decimal places.
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58
The density function for the time to complete a certain task is approximately equal to The density function for the time to complete a certain task is approximately equal to , where t is time in minutes and . A. Find the median number of minutes taken, to 2 decimal places. B. Find the mean number of minutes taken, to 2 decimal places. , where t is time in minutes and The density function for the time to complete a certain task is approximately equal to , where t is time in minutes and . A. Find the median number of minutes taken, to 2 decimal places. B. Find the mean number of minutes taken, to 2 decimal places. .
A. Find the median number of minutes taken, to 2 decimal places.
B. Find the mean number of minutes taken, to 2 decimal places.
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59
A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: A professor far away from here gives the same 100-point final exam year after year and discovers that the students' scores tend to follow the triangular probability density function f(x) pictured below: Do the mean and the median both describe the same point on this probability density function? Do the mean and the median both describe the same point on this probability density function?
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60
Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. Suppose that the distribution of people's ages in the United States is essentially constant, or uniform, from age 0 to age 60, and from there it decreases linearly until age 100. This distribution p(x) is shown below, where x is age in years, and p measures probability density. Such a probability distribution is called trapezoidal. Find the median age of the United States population. Find the median age of the United States population.
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61
Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?

A) <strong>Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?</strong> A) B) C) D)
B) <strong>Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?</strong> A) B) C) D)
C) <strong>Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?</strong> A) B) C) D)
D) <strong>Which of the following distributions best describe the density function for annual popcorn sales by a Cub Scout pack if the sales are approximately normally distributed and they almost always make between $300 and $500?</strong> A) B) C) D)
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62
Let Let be the density function for call-back time by an answering service with t = time in minutes and . Find the mean, in minutes, to 2 decimal places. be the density function for call-back time by an answering service with t = time in minutes and Let be the density function for call-back time by an answering service with t = time in minutes and . Find the mean, in minutes, to 2 decimal places. . Find the mean, in minutes, to 2 decimal places.
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63
The number of hours of sleep per night averaged by a group of students is approximately normally distributed with mean The number of hours of sleep per night averaged by a group of students is approximately normally distributed with mean and standard deviation . What is the probability that a student selected at random had more than 7.5 hours of sleep? Round to 2 decimal places. and standard deviation The number of hours of sleep per night averaged by a group of students is approximately normally distributed with mean and standard deviation . What is the probability that a student selected at random had more than 7.5 hours of sleep? Round to 2 decimal places. . What is the probability that a student selected at random had more than 7.5 hours of sleep? Round to 2 decimal places.
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64
The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function and the corresponding cumulative distribution function , where t is time in minutes. Express in terms of . and the corresponding cumulative distribution function The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function and the corresponding cumulative distribution function , where t is time in minutes. Express in terms of . , where t is time in minutes. Express The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function and the corresponding cumulative distribution function , where t is time in minutes. Express in terms of . in terms of The race times for a group of cross-country runners are all between 15 and 25 minutes. They are represented by the density function and the corresponding cumulative distribution function , where t is time in minutes. Express in terms of . .
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65
The speed of cars on a freeway are approximately normally distributed with mean The speed of cars on a freeway are approximately normally distributed with mean mph and standard deviation mph. Assume a maximum speed of 100 mph. What percent of cars are going between 65 and 70 mph? Round to the nearest percent. mph and standard deviation The speed of cars on a freeway are approximately normally distributed with mean mph and standard deviation mph. Assume a maximum speed of 100 mph. What percent of cars are going between 65 and 70 mph? Round to the nearest percent. mph. Assume a maximum speed of 100 mph. What percent of cars are going between 65 and 70 mph? Round to the nearest percent.
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66
The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. Which figure is the cumulative distribution function?
I. The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. Which figure is the cumulative distribution function? I. II. II. The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. Which figure is the cumulative distribution function? I. II.
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67
The speed of cars on a freeway are approximately normally distributed with mean The speed of cars on a freeway are approximately normally distributed with mean mph and standard deviation mph. Assume a maximum speed of 100 mph. If speeding tickets are given to cars traveling faster than 82 mph, what is the probability that a randomly selected car is going fast enough to get a ticket? Round to 2 decimal places. mph and standard deviation The speed of cars on a freeway are approximately normally distributed with mean mph and standard deviation mph. Assume a maximum speed of 100 mph. If speeding tickets are given to cars traveling faster than 82 mph, what is the probability that a randomly selected car is going fast enough to get a ticket? Round to 2 decimal places. mph. Assume a maximum speed of 100 mph. If speeding tickets are given to cars traveling faster than 82 mph, what is the probability that a randomly selected car is going fast enough to get a ticket? Round to 2 decimal places.
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68
The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. About what percent of the people in the school are adults? I. <strong>The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. About what percent of the people in the school are adults? I. II. </strong> A)20% B)40% C)60% D)80% II. <strong>The density function and the cumulative distribution function for the ages of people in an elementary school are graphed below. About what percent of the people in the school are adults? I. II. </strong> A)20% B)40% C)60% D)80%

A)20%
B)40%
C)60%
D)80%
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