Question 1

Find the mean of the scores. ​
7, 3, 4, 1, 6, 3
​

Accepted Answer

A) 3.5 
B) 4 
C) 3 
D) 2.5 
E) 6 
A) 3.5 
B) 4 
C) 3 
D) 2.5 
E) 6 B

Question 2

Use a table of the standard normal distribution to find the probability that a z-score from the standard normal distribution will lie within the interval   . Round your answer to four decimal places. ​

Accepted Answer

A) 0.4969 
B) 0.0062 
C) 0.6625 
D) 0.9938 
E) 0.4938 
A) 0.4969 
B) 0.0062 
C) 0.6625 
D) 0.9938 
E) 0.4938 D

Question 3

The Fish Commission states that the lengths of all fish in Spring Run are normally distributed, with mean 18 cm and standard deviation 5 cm. What is the probability that a fish caught in Spring Run will be between 18 and 25.5 cm long? Round your answer to four decimal places. ​

Accepted Answer

A) 0.9332 
B) 0.4332 
C) 0.5668 
D) 0.0668 
E) 0.8664 
A) 0.9332 
B) 0.4332 
C) 0.5668 
D) 0.0668 
E) 0.8664 B

Question 4

In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 9,000 tons and a standard deviation of 1,000 tons. Find the probability that on a randomly selected day the amount of industrial waste is less than 7,000 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A) 0.9772 
B) 0.1836 
C) 0.7936 
D) 0.0228 
E) 0.7720 
A) 0.9772 
B) 0.1836 
C) 0.7936 
D) 0.0228 
E) 0.7720

Question 5

Reaction time for a group of people is normally distributed, with a mean of 0.9 seconds and a standard deviation of 0.1 seconds. Find the probability that an individual selected at random has a reaction time less than 1 second. Round your answer to four decimal places. ​

Accepted Answer

A) 0.3413 
B) 0.6587 
C) 0.1587 
D) 0.8413 
E) 0.6826 
A) 0.3413 
B) 0.6587 
C) 0.1587 
D) 0.8413 
E) 0.6826

Question 6

A family has 5 children. If the probability that each child is a girl is 0.5, what is the probability that 4 of the children are girls? Round your answer to six decimal places. ​

Accepted Answer

A) Pr(4 Girls) = 0.078125 
B) Pr(4 Girls) = 0.039063 
C) Pr(4 Girls) = 0.156250 
D) Pr(4 Girls) = 0.062500 
E) Pr(4 Girls) = 0.125000 
A) Pr(4 Girls) = 0.078125 
B) Pr(4 Girls) = 0.039063 
C) Pr(4 Girls) = 0.156250 
D) Pr(4 Girls) = 0.062500 
E) Pr(4 Girls) = 0.125000

Question 7

If a fair coin is tossed 123 times, what is the probability that no more than 67 heads will occur? Round your answer to four decimal places. ​

Accepted Answer

A) 0.5141 
B) 0.6483 
C) 0.1401 
D) 0.7738 
E) 0.8599 
A) 0.5141 
B) 0.6483 
C) 0.1401 
D) 0.7738 
E) 0.8599

Question 8

The mean weight of a group of boys is 150 lb, with a standard deviation of 20 lb. If the weights are normally distributed, find the probability that one of the boys picked at random from the group weighs more than 178 lb. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A) ​0.9192 
B) ​0.4192 
C) ​0.4278 
D) ​0.2318 
E) ​0.0808 
A) ​0.9192 
B) ​0.4192 
C) ​0.4278 
D) ​0.2318 
E) ​0.0808

Question 9

Suppose a pair of dice is thrown 11 times. What is the probability that a sum of 10 occurs exactly 4 times? Round your answer to six decimal places. ​

Accepted Answer

A) 0.022053 
B) 0.043112 
C) 0.071062 
D) 0.008655 
E) 0.103840 
A) 0.022053 
B) 0.043112 
C) 0.071062 
D) 0.008655 
E) 0.103840

Question 10

Systolic blood pressure for a group of women is normally distributed, with a mean of 120 and a standard deviation of 15. Find the probability that a woman selected at random has blood pressure greater than 142.5. Round your answer to four decimal places. ​

Accepted Answer

A) 0.9332 
B) 0.5668 
C) 0.0668 
D) 0.4332 
E) 0.8664 
A) 0.9332 
B) 0.5668 
C) 0.0668 
D) 0.4332 
E) 0.8664

Question 11

Determine y, if possible, so that the table describes a discrete probability distribution. ​   ​

Accepted Answer

A) y =   
B) ​y =   
C)    
D)    
E) not possible 
A) y =   
B) ​y =   
C)    
D)    
E) not possible

Question 12

In a certain school district, 23% of the faculty use none of their sick days in a school year. Find the probability that 4 faculty members selected at random used no sick days in a given year. Round your answer to eight decimal places. ​

Accepted Answer

A) 0.00279841 
B) 0.01216700 
C) 0.00064363 
D) 0.35153041 
E) 0.45653300 
A) 0.00279841 
B) 0.01216700 
C) 0.00064363 
D) 0.35153041 
E) 0.45653300

Question 13

Determine c, if possible, so that the formula   describes a discrete probability distribution. ​

Accepted Answer

A) 2 
B)    
C) 194 
D) 33 
E) not possible 
A) 2 
B)    
C) 194 
D) 33 
E) not possible

Question 14

A bag contains 6 red balls and 6 black balls. We draw 6 balls, with each one replaced before the next is drawn. What is the probability that at least 4 black balls will be drawn? Round your answer to five decimal places. ​

Accepted Answer

A) 0.23438 
B) 0.09375 
C) 0.01563 
D) 0.32813 
E) 0.34375 
A) 0.23438 
B) 0.09375 
C) 0.01563 
D) 0.32813 
E) 0.34375

Question 15

Which frequency histogram best describes the data given in the frequency table? ​
Age
Frequency
1-4
6
5-8
9
9-12
3
13-16
1
17-20
4
​

Accepted Answer

A) ​   
B) ​ ​   
C) ​ ​​   
D) ​ ​   
E) ​ ​   
A) ​   
B) ​ ​   
C) ​ ​​   
D) ​ ​   
E) ​ ​

Question 16

In a binomial experiment, find the probability of between 33 and 38 successes in 150 trials if   . Round your answer to four decimal places. ​

Accepted Answer

A) 0.2641 
B) 0.7359 
C) 0.1321 
D) 0.3962 
E) 0.0660 
A) 0.2641 
B) 0.7359 
C) 0.1321 
D) 0.3962 
E) 0.0660

Question 17

A car owner must decide whether she should take out a $100-deductible collision policy in addition to her liability insurance policy. Records show that each year, in her area, 17% of the drivers have an accident that is their fault or for which no fault is assigned, and that the average cost of repairs for these types of accidents is $1200. If the $100-deductible collision policy costs $100 per year, would she save money in the long run by buying the insurance or "taking the chance"? (Hint: Find the expected values if she has the policy and if she doesn't have the policy and compare them.) ​

Accepted Answer

A) by buying the insurance 
B) by taking the chance 
A) by buying the insurance 
B) by taking the chance

Question 18

Suppose the probability that a certain drug will lower cholesterol significantly is 0.85. If the drug is administered to 1300 patients, what is the probability that more than 1094 will have significantly lowered cholesterol levels? Round your answer to four decimal places. ​

Accepted Answer

A) 0.2073 
B) 0.7894 
C) 0.6828 
D) 0.7550 
E) 0.7927 
A) 0.2073 
B) 0.7894 
C) 0.6828 
D) 0.7550 
E) 0.7927

Question 19

A young man plans to sell umbrellas at the city's Easter Parade. He knows that he can sell 152 umbrellas at $14 each if it rains hard, he can sell 108 if it rains lightly, and he can sell 41 if it doesn't rain at all. Past records show it rains hard 28% of the time on Easter, rains lightly 69% of the time, and does not rain at all 3% of the time. If he can buy 0, 100, or 200 umbrellas at $5 each and return the unsold ones for $3 each, how many should he buy? ​

Accepted Answer

A) 200 umbrellas 
B) 100 umbrellas 
A) 200 umbrellas 
B) 100 umbrellas

Question 20

Determine c, if possible, so that the formula   describes a discrete probability distribution. ​

Accepted Answer

A) 11 
B)    
C) 35 
D) ​   
E) not possible 
A) 11 
B)    
C) 35 
D) ​   
E) not possible

Find the mean of the scores. 7, 3, 4, 1, 6, 3

Use a table of the standard normal distribution to find the probability that a z-score from the standard normal distribution will lie within the interval . Round your answer to four decimal places.

The Fish Commission states that the lengths of all fish in Spring Run are normally distributed, with mean 18 cm and standard deviation 5 cm. What is the probability that a fish caught in Spring Run will be between 18 and 25.5 cm long? Round your answer to four decimal places.

Reaction time for a group of people is normally distributed, with a mean of 0.9 seconds and a standard deviation of 0.1 seconds. Find the probability that an individual selected at random has a reaction time less than 1 second. Round your answer to four decimal places.

A family has 5 children. If the probability that each child is a girl is 0.5, what is the probability that 4 of the children are girls? Round your answer to six decimal places.

If a fair coin is tossed 123 times, what is the probability that no more than 67 heads will occur? Round your answer to four decimal places.

Suppose a pair of dice is thrown 11 times. What is the probability that a sum of 10 occurs exactly 4 times? Round your answer to six decimal places.

Systolic blood pressure for a group of women is normally distributed, with a mean of 120 and a standard deviation of 15. Find the probability that a woman selected at random has blood pressure greater than 142.5. Round your answer to four decimal places.

Determine y, if possible, so that the table describes a discrete probability distribution.

In a certain school district, 23% of the faculty use none of their sick days in a school year. Find the probability that 4 faculty members selected at random used no sick days in a given year. Round your answer to eight decimal places.

Determine c, if possible, so that the formula describes a discrete probability distribution.

A bag contains 6 red balls and 6 black balls. We draw 6 balls, with each one replaced before the next is drawn. What is the probability that at least 4 black balls will be drawn? Round your answer to five decimal places.

Which frequency histogram best describes the data given in the frequency table? Age Frequency 1-4 6 5-8 9 9-12 3 13-16 1 17-20 4

In a binomial experiment, find the probability of between 33 and 38 successes in 150 trials if . Round your answer to four decimal places.

Suppose the probability that a certain drug will lower cholesterol significantly is 0.85. If the drug is administered to 1300 patients, what is the probability that more than 1094 will have significantly lowered cholesterol levels? Round your answer to four decimal places.

Determine c, if possible, so that the formula describes a discrete probability distribution.

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 9: Further Topics in Probability; Data Description

Find the mean of the scores. ​ 7, 3, 4, 1, 6, 3 ​

Use a table of the standard normal distribution to find the probability that a z-score from the standard normal distribution will lie within the interval . Round your answer to four decimal places. ​

The Fish Commission states that the lengths of all fish in Spring Run are normally distributed, with mean 18 cm and standard deviation 5 cm. What is the probability that a fish caught in Spring Run will be between 18 and 25.5 cm long? Round your answer to four decimal places. ​

Reaction time for a group of people is normally distributed, with a mean of 0.9 seconds and a standard deviation of 0.1 seconds. Find the probability that an individual selected at random has a reaction time less than 1 second. Round your answer to four decimal places. ​

A family has 5 children. If the probability that each child is a girl is 0.5, what is the probability that 4 of the children are girls? Round your answer to six decimal places. ​

If a fair coin is tossed 123 times, what is the probability that no more than 67 heads will occur? Round your answer to four decimal places. ​

Suppose a pair of dice is thrown 11 times. What is the probability that a sum of 10 occurs exactly 4 times? Round your answer to six decimal places. ​

Systolic blood pressure for a group of women is normally distributed, with a mean of 120 and a standard deviation of 15. Find the probability that a woman selected at random has blood pressure greater than 142.5. Round your answer to four decimal places. ​

Determine y, if possible, so that the table describes a discrete probability distribution. ​ ​

In a certain school district, 23% of the faculty use none of their sick days in a school year. Find the probability that 4 faculty members selected at random used no sick days in a given year. Round your answer to eight decimal places. ​

Determine c, if possible, so that the formula describes a discrete probability distribution. ​

A bag contains 6 red balls and 6 black balls. We draw 6 balls, with each one replaced before the next is drawn. What is the probability that at least 4 black balls will be drawn? Round your answer to five decimal places. ​

Which frequency histogram best describes the data given in the frequency table? ​ Age Frequency 1-4 6 5-8 9 9-12 3 13-16 1 17-20 4 ​

In a binomial experiment, find the probability of between 33 and 38 successes in 150 trials if . Round your answer to four decimal places. ​

Suppose the probability that a certain drug will lower cholesterol significantly is 0.85. If the drug is administered to 1300 patients, what is the probability that more than 1094 will have significantly lowered cholesterol levels? Round your answer to four decimal places. ​

Determine c, if possible, so that the formula describes a discrete probability distribution. ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Find the mean of the scores. 7, 3, 4, 1, 6, 3

Use a table of the standard normal distribution to find the probability that a z-score from the standard normal distribution will lie within the interval . Round your answer to four decimal places.

The Fish Commission states that the lengths of all fish in Spring Run are normally distributed, with mean 18 cm and standard deviation 5 cm. What is the probability that a fish caught in Spring Run will be between 18 and 25.5 cm long? Round your answer to four decimal places.

Reaction time for a group of people is normally distributed, with a mean of 0.9 seconds and a standard deviation of 0.1 seconds. Find the probability that an individual selected at random has a reaction time less than 1 second. Round your answer to four decimal places.

A family has 5 children. If the probability that each child is a girl is 0.5, what is the probability that 4 of the children are girls? Round your answer to six decimal places.

If a fair coin is tossed 123 times, what is the probability that no more than 67 heads will occur? Round your answer to four decimal places.

Suppose a pair of dice is thrown 11 times. What is the probability that a sum of 10 occurs exactly 4 times? Round your answer to six decimal places.

Systolic blood pressure for a group of women is normally distributed, with a mean of 120 and a standard deviation of 15. Find the probability that a woman selected at random has blood pressure greater than 142.5. Round your answer to four decimal places.

Determine y, if possible, so that the table describes a discrete probability distribution.

In a certain school district, 23% of the faculty use none of their sick days in a school year. Find the probability that 4 faculty members selected at random used no sick days in a given year. Round your answer to eight decimal places.

Determine c, if possible, so that the formula describes a discrete probability distribution.

A bag contains 6 red balls and 6 black balls. We draw 6 balls, with each one replaced before the next is drawn. What is the probability that at least 4 black balls will be drawn? Round your answer to five decimal places.

Which frequency histogram best describes the data given in the frequency table? Age Frequency 1-4 6 5-8 9 9-12 3 13-16 1 17-20 4

In a binomial experiment, find the probability of between 33 and 38 successes in 150 trials if . Round your answer to four decimal places.

Suppose the probability that a certain drug will lower cholesterol significantly is 0.85. If the drug is administered to 1300 patients, what is the probability that more than 1094 will have significantly lowered cholesterol levels? Round your answer to four decimal places.

Determine c, if possible, so that the formula describes a discrete probability distribution.