Question 1

When the points on a normal probability plot lie approximately on a straight line, the data are approximately normally distributed.

Accepted Answer

A) True 
 B)False

Question 2

The exponential distribution has the property that its mean equals its standard deviation.

Accepted Answer

A) True 
 B)False

Question 3

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1700 miles. What is the probability a certain tire of this brand will last between 56,430 miles and 56,940 miles?

Accepted Answer

A)  .0180 
B)  .9813 
C)  .4920 
D)  .4649 
A)  .0180 
B)  .9813 
C)  .4920 
D)  .4649

Question 4

The rate of return for an investment can be described by a normal distribution with mean 47% and standard deviation 3%. What is the probability that the rate of return for the investment exceeds 53%?

Accepted Answer

Let x be the rate of return. Then x is a

Question 5

Suppose x is a random variable best described by a uniform probability distribution with c = 60 and d = 20. Find P(x ≥ 60).

Accepted Answer

A)  1 
B)  0 
C)  0.5 
D)  0.4 
A)  1 
B)  0 
C)  0.5 
D)  0.4

Question 6

For any continuous probability distribution, P(x = c) = 0 for all values of c.

Accepted Answer

A) True 
 B)False

Question 7

Use the standard normal distribution to find $$P ( - 2.50 < z < 1.50 )$$

Accepted Answer

A)  .9270 
B)  .8822 
C)  .6167 
D)  .5496 
A)  .9270 
B)  .8822 
C)  .6167 
D)  .5496

Question 8

Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 538 and 546 drivers in a sample of 700 drivers wear seat belts?

Accepted Answer

A)  0.0837 
B)  0.0166 
C)  0.1003 
D)  0.8997 
A)  0.0837 
B)  0.0166 
C)  0.1003 
D)  0.8997

Question 9

It is against the law to discriminate against job applicants because of race, religion, sex, or age. Of the individuals who apply for an accountant's position in a large corporation, 39% are over 45 years old. If the company decides to choose 96 of a very large number of applicants for closer credential screening, claiming that the selection will be random and not age-biased, what is the z-value associated with fewer than 46 of those chosen being over 45 years old? (Assume that the applicant pool is large enough so that x, the number in the sample over 45 years old, has a binomial probability distribution.)

Accepted Answer

x is a binomial rand

Question 10

Suppose x is a uniform random variable with c = 10 and d = 80. Find the mean of the random variable x.

Accepted Answer

The answer of Suppose x is a uniform random variable...

Question 11

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2300 miles. What is the probability a particular tire of this brand will last longer than 57,700 miles?

Accepted Answer

A)  .8413 
B)  .1587 
C)  .2266 
D)  .7266 
A)  .8413 
B)  .1587 
C)  .2266 
D)  .7266

Question 12

Determine the value of $e ^ { - a / \theta } \text { for } \theta = 2 \text { and } a = 3$

Accepted Answer

A)  0.223130 
B)  0.513417 
C)  -4.481689 
D)  4.481689 
A)  0.223130 
B)  0.513417 
C)  -4.481689 
D)  4.481689

Question 13

The number of children in a family can be modelled using a continuous random variable.

Accepted Answer

A) True 
 B)False

Question 14

Farmers often sell fruits and vegetables at roadside stands during the summer. One such roadside stand has a daily demand for tomatoes that is approximately normally distributed with a mean of 124 tomatoes and a standard deviation of 30 tomatoes. How many tomatoes must be available on any given day so that there is only a 1.5% chance that all tomatoes will be sold?

Accepted Answer

The answer of Farmers often sell fruits and vegetables at...

Question 15

The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 24.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?

Accepted Answer

A)  .9938 
B)  .4938 
C)  .0062 
D)  .5062 
A)  .9938 
B)  .4938 
C)  .0062 
D)  .5062

Question 16

Use the standard normal distribution to find $$\mathrm { P } ( \mathrm { z }  2.33 )$$

Accepted Answer

A)  .0198 
B)  .9809 
C)  .7888 
D)  .0606 
A)  .0198 
B)  .9809 
C)  .7888 
D)  .0606

Question 17

Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find P(800 < x ≤ 820).

Accepted Answer

A)  0.4314 
B)  0.4222 
C)  0.4474 
D)  0.0517 
A)  0.4314 
B)  0.4222 
C)  0.4474 
D)  0.0517

Question 18

Suppose a random variable x is best described by a normal distribution with $\mu = 60 \text { and } \sigma = 5 \text {. }$ . Find the z-score that corresponds to the value x = 65.

Accepted Answer

A)  1 
B)  5 
C)  65 
D)  12 
A)  1 
B)  5 
C)  65 
D)  12

Question 19

A statistician received some data to analyze. The sender of the data suggested that the data was normally distributed. Which of the following methods can be used to determine if the data is, in fact, normally distributed? I. Construct a histogram and/or stem-and-leaf display of the data and check the shape.
II. Compute the intervals $\bar { x } \pm s , \bar { x } \pm 2 s$, and $\bar { x } \pm 3 s$, and determine the percentage of measurements falling in each. Compare these percentages to $68 \% , 95 \%$, and $100 \%$.
III. Calculate a value of $\frac { \mathrm { IQR } } { \mathrm { s } }$. If this value is approximately $1.3$, then the data is normal.
IV. Construct a normal probability plot of the data. If the points fall on a straight line, then the data is normal.

Accepted Answer

A)  I only 
B)  II only 
C)  III only 
D)  IV only 
E)  I, II, III, and IV 
A)  I only 
B)  II only 
C)  III only 
D)  IV only 
E)  I, II, III, and IV

When the points on a normal probability plot lie approximately on a straight line, the data are approximately normally distributed.

The exponential distribution has the property that its mean equals its standard deviation.

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1700 miles. What is the probability a certain tire of this brand will last between 56,430 miles and 56,940 miles?

The rate of return for an investment can be described by a normal distribution with mean 47% and standard deviation 3%. What is the probability that the rate of return for the investment exceeds 53%?

Suppose x is a random variable best described by a uniform probability distribution with c = 60 and d = 20. Find P(x ≥ 60).

For any continuous probability distribution, P(x = c) = 0 for all values of c.

Use the standard normal distribution to find $P ( - 2.50 < z < 1.50 )$

Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 538 and 546 drivers in a sample of 700 drivers wear seat belts?

Suppose x is a uniform random variable with c = 10 and d = 80. Find the mean of the random variable x.

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2300 miles. What is the probability a particular tire of this brand will last longer than 57,700 miles?

Determine the value of $e ^ { - a / \theta } \text { for } \theta = 2 \text { and } a = 3$

The number of children in a family can be modelled using a continuous random variable.

The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 24.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?

Use the standard normal distribution to find $\mathrm { P } ( \mathrm { z } < - 2.33 \text { or } \mathrm { z } > 2.33 )$

Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find P(800 < x ≤ 820).

Suppose a random variable x is best described by a normal distribution with $\mu = 60 \text { and } \sigma = 5 \text {. }$ . Find the z-score that corresponds to the value x = 65.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Discrete Random Variables

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: Tests of Hypothesis

Inferences Based on a Two Samples: Confidence Intervals and Tests of Hypotheses

Analysis of Variance: Comparing More Than Two Means

Simple Linear Regression

Multiple Regression and Model Building

Categorical Data Analysis

Nonparametric Statistics

Filters

Exam 5: Continuous Random Variables

When the points on a normal probability plot lie approximately on a straight line, the data are approximately normally distributed.

The exponential distribution has the property that its mean equals its standard deviation.

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1700 miles. What is the probability a certain tire of this brand will last between 56,430 miles and 56,940 miles?

The rate of return for an investment can be described by a normal distribution with mean 47% and standard deviation 3%. What is the probability that the rate of return for the investment exceeds 53%?

Suppose x is a random variable best described by a uniform probability distribution with c = 60 and d = 20. Find P(x ≥ 60).

For any continuous probability distribution, P(x = c) = 0 for all values of c.

Use the standard normal distribution to find P(−2.50<z<1.50)P ( - 2.50 < z < 1.50 )P(−2.50<z<1.50)

Transportation officials tell us that 80% of drivers wear seat belts while driving. What is the probability that between 538 and 546 drivers in a sample of 700 drivers wear seat belts?

Suppose x is a uniform random variable with c = 10 and d = 80. Find the mean of the random variable x.

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2300 miles. What is the probability a particular tire of this brand will last longer than 57,700 miles?

Determine the value of e−a/θ for θ=2 and a=3e ^ { - a / \theta } \text { for } \theta = 2 \text { and } a = 3e−a/θ for θ=2 and a=3

The number of children in a family can be modelled using a continuous random variable.

The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 24.5 ounces and a standard deviation of 0.2 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?

Use the standard normal distribution to find P(z<−2.33 or z>2.33)\mathrm { P } ( \mathrm { z } < - 2.33 \text { or } \mathrm { z } > 2.33 )P(z<−2.33 or z>2.33)

Assume that x is a binomial random variable with n = 1000 and p = 0.80. Use a normal approximation to find P(800 < x ≤ 820).

Suppose a random variable x is best described by a normal distribution with μ=60 and σ=5. \mu = 60 \text { and } \sigma = 5 \text {. }μ=60 and σ=5. . Find the z-score that corresponds to the value x = 65.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Discrete Random Variables

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: Tests of Hypothesis

Inferences Based on a Two Samples: Confidence Intervals and Tests of Hypotheses

Analysis of Variance: Comparing More Than Two Means

Simple Linear Regression

Multiple Regression and Model Building

Categorical Data Analysis

Nonparametric Statistics

Filters

Use the standard normal distribution to find $P ( - 2.50 < z < 1.50 )$

Determine the value of $e ^ { - a / \theta } \text { for } \theta = 2 \text { and } a = 3$

Use the standard normal distribution to find $\mathrm { P } ( \mathrm { z } < - 2.33 \text { or } \mathrm { z } > 2.33 )$

Suppose a random variable x is best described by a normal distribution with $\mu = 60 \text { and } \sigma = 5 \text {. }$ . Find the z-score that corresponds to the value x = 65.