Question 1

Find the mode(s) of the scores. ​
11, 12, 14, 10, 18, 12, 13, 14
​

Accepted Answer

A) 12 
B) 12, 13 
C) 13 
D) 14 
E) 12, 14 
A) 12 
B) 12, 13 
C) 13 
D) 14 
E) 12, 14

Question 2

Suppose the probability that a marksman will hit a target each time he shoots is 0.67. If he fires 7 shots at a target, what is the probability he will hit it 2 times? Round your answer to six decimal places. ​

Accepted Answer

A) Pr(2 Hits) = 0.036893 
B) Pr(2 Hits) = 0.008950 
C) Pr(2 Hits) = 0.000615 
D) Pr(2 Hits) = 0.012298 
E) Pr(2 Hits) = 0.006149 
A) Pr(2 Hits) = 0.036893 
B) Pr(2 Hits) = 0.008950 
C) Pr(2 Hits) = 0.000615 
D) Pr(2 Hits) = 0.012298 
E) Pr(2 Hits) = 0.006149

Question 3

In studying a certain endangered species, scientists have found that when the animals are relocated, it takes x years without offspring before the first young are born, where x and the probability of x are given below. What is the expected number of years before the first young are born? ​   ​

Accepted Answer

A) 1.96 years 
B) 0.96 years 
C) 0.64 years 
D) 1.56 years 
E) 1.68 years 
A) 1.96 years 
B) 0.96 years 
C) 0.64 years 
D) 1.56 years 
E) 1.68 years

Question 4

If records indicate that 8 houses out of 1000 are expected to be damaged by fire in any year, what is the probability that a woman who owns 16 houses will have fire damage in 2 of them in a year? Round your answers to six decimal places. ​

Accepted Answer

A) Pr(2 Fires) = 0.003432 
B) Pr(2 Fires) = 0.006863 
C) Pr(2 Fires) = 0.034316 
D) Pr(2 Fires) = 0.005719 
E) Pr(2 Fires) = 0.013726 
A) Pr(2 Fires) = 0.003432 
B) Pr(2 Fires) = 0.006863 
C) Pr(2 Fires) = 0.034316 
D) Pr(2 Fires) = 0.005719 
E) Pr(2 Fires) = 0.013726

Question 5

Suppose a fair die is rolled 10 times. What is the probability that a 6 will occur 3 times in the 10 rolls? Round your answer to six decimal places. ​

Accepted Answer

A) Pr(3 6-es) = 0.310091 
B) Pr(3 6-es) = 0.155045 
C) Pr(3 6-es) = 0.387613 
D) Pr(3 6-es) = 0.232568 
E) Pr(3 6-es) = 0.193807 
A) Pr(3 6-es) = 0.310091 
B) Pr(3 6-es) = 0.155045 
C) Pr(3 6-es) = 0.387613 
D) Pr(3 6-es) = 0.232568 
E) Pr(3 6-es) = 0.193807

Question 6

It has been determined empirically that the probability that a given cell will survive for a given period of time is 0.65. Find the probability that 3 out of 7 of these cells will survive for this period of time. Round your answer to six decimal places. ​

Accepted Answer

A) Pr(3 Survive) = 0.072119 
B) Pr(3 Survive) = 0.096159 
C) Pr(3 Survive) = 0.144238 
D) Pr(3 Survive) = 0.057695 
E) Pr(3 Survive) = 0.125425 
A) Pr(3 Survive) = 0.072119 
B) Pr(3 Survive) = 0.096159 
C) Pr(3 Survive) = 0.144238 
D) Pr(3 Survive) = 0.057695 
E) Pr(3 Survive) = 0.125425

Question 7

The probability that a certain couple will have a blue-eyed child is   , and they have 5 children. What is the probability that none of their children have blue eyes? Round your answer to six decimal places. ​

Accepted Answer

A) Pr(0 Blue) = 0 
B) Pr(0 Blue) = 0.001978 
C) Pr(0 Blue) = 0.000260 
D) Pr(0 Blue) = 0.000648 
E) Pr(0 Blue) = 1 
A) Pr(0 Blue) = 0 
B) Pr(0 Blue) = 0.001978 
C) Pr(0 Blue) = 0.000260 
D) Pr(0 Blue) = 0.000648 
E) Pr(0 Blue) = 1

Question 8

Suppose a pair of dice is thrown 950 times. Estimate how many times would we expect a sum of 5 to occur? Round your answer to the nearest integer. ​

Accepted Answer

A) 844 times 
B) 633 times 
C) 106 times 
D) 158 times 
E) 132 times 
A) 844 times 
B) 633 times 
C) 106 times 
D) 158 times 
E) 132 times

Question 9

In a binomial experiment find the probability of at least 43 successes in 110 trials if   . Round your answer to four decimal places. ​

Accepted Answer

A) 0.9761 
B) 0.4511 
C) 0.0239 
D) 0.4560 
E) 0.1853 
A) 0.9761 
B) 0.4511 
C) 0.0239 
D) 0.4560 
E) 0.1853

Question 10

Suppose a report by U.S. News and World Report states that 25% of all employee credentials examined were falsified. If this is true, what is the probability that at least 79 of 240 employees hired during a year had falsified their credentials? Round your answer to four decimal places. ​

Accepted Answer

A) ​0.2594 
B) ​0.9971 
C) ​0.0029 
D) ​0.0366 
E) ​0.0042 
A) ​0.2594 
B) ​0.9971 
C) ​0.0029 
D) ​0.0366 
E) ​0.0042

Question 11

In a certain state, the daily amounts of industrial waste are normally distributed, with a mean of 5,000 tons and a standard deviation of 1,500 tons. Find the probability that on a randomly selected day the amount of industrial waste is greater than 6,695 tons. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A) ​0.1292 
B) ​0.8708 
C) ​0.5050 
D) ​0.3609 
E) ​0.3876 
A) ​0.1292 
B) ​0.8708 
C) ​0.5050 
D) ​0.3609 
E) ​0.3876

Question 12

In a binomial experiment find the probability of no more than 89 successes in 114 trials if   . Round your answer to four decimal places. ​

Accepted Answer

A) 0.6305 
B) 0.0239 
C) 0.4761 
D) 0.7337 
E) 0.9761 
A) 0.6305 
B) 0.0239 
C) 0.4761 
D) 0.7337 
E) 0.9761

Question 13

Find the mode of the set of scores. ​
6, 11, 12, 6, 7, 5, 6, 5
​

Accepted Answer

A) 6 
B) 7.25 
C) 5 
D) 8 
E) 7 
A) 6 
B) 7.25 
C) 5 
D) 8 
E) 7

Question 14

Suppose an experiment has five possible outcomes for x: 1, 2, 3, 4, 5. The probability that each of these outcomes occurs is   . Estimate the expected value of x for the experiment to two decimal places? ​

Accepted Answer

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

Question 15

A die is rolled 2 times, and success is rolling a number greater than 3. Let x = ​number of success. Construct the binomial distribution that describes this experiment, and find the mean of this distribution. ​

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 16

Suppose a fair coin is tossed 12 times. What is the probability that exactly 10 heads will occur? ​

Accepted Answer

A) Pr(10 Heads) =   
B) Pr(10 Heads) =   
C) Pr(10 Heads) =   
D) Pr(10 Heads) =   
E) Pr(10 Heads) =   
A) Pr(10 Heads) =   
B) Pr(10 Heads) =   
C) Pr(10 Heads) =   
D) Pr(10 Heads) =   
E) Pr(10 Heads) =

Question 17

In a binomial experiment, find the probability 51 of 71 successes in trials if   . Round your answer to four decimal places. ​

Accepted Answer

A) ​0.9880 
B) ​0.0120 
C) ​0.9820 
D) ​0.3328 
E) ​0.9910 
A) ​0.9880 
B) ​0.0120 
C) ​0.9820 
D) ​0.3328 
E) ​0.9910

Question 18

In a binomial experiment, find the probability of more than 43 successes in 110 trials if   . Round your answer to four decimal places. ​

Accepted Answer

A) 0.9854 
B) 0.2722 
C) 0.2194 
D) 0.3569 
E) 0.0146 
A) 0.9854 
B) 0.2722 
C) 0.2194 
D) 0.3569 
E) 0.0146

Question 19

A coin is "loaded" so that the probability of tossing a head is   . If it is tossed 50 times, what are the mean and the standard deviation of the number of heads that occur? ​

Accepted Answer

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

Question 20

Suppose a population of scores x is normally distributed with   and   Use the standard normal distribution to find   . Round your answer to four decimal places. ​

Accepted Answer

A) 0.0980 
B) 0.1378 
C) 0.2358 
D) 0.0398 
E) 0.1179 
A) 0.0980 
B) 0.1378 
C) 0.2358 
D) 0.0398 
E) 0.1179

Find the mode(s) of the scores. 11, 12, 14, 10, 18, 12, 13, 14

Suppose the probability that a marksman will hit a target each time he shoots is 0.67. If he fires 7 shots at a target, what is the probability he will hit it 2 times? Round your answer to six decimal places.

In studying a certain endangered species, scientists have found that when the animals are relocated, it takes x years without offspring before the first young are born, where x and the probability of x are given below. What is the expected number of years before the first young are born?

If records indicate that 8 houses out of 1000 are expected to be damaged by fire in any year, what is the probability that a woman who owns 16 houses will have fire damage in 2 of them in a year? Round your answers to six decimal places.

Suppose a fair die is rolled 10 times. What is the probability that a 6 will occur 3 times in the 10 rolls? Round your answer to six decimal places.

It has been determined empirically that the probability that a given cell will survive for a given period of time is 0.65. Find the probability that 3 out of 7 of these cells will survive for this period of time. Round your answer to six decimal places.

The probability that a certain couple will have a blue-eyed child is , and they have 5 children. What is the probability that none of their children have blue eyes? Round your answer to six decimal places.

Suppose a pair of dice is thrown 950 times. Estimate how many times would we expect a sum of 5 to occur? Round your answer to the nearest integer.

In a binomial experiment find the probability of at least 43 successes in 110 trials if . Round your answer to four decimal places.

Suppose a report by U.S. News and World Report states that 25% of all employee credentials examined were falsified. If this is true, what is the probability that at least 79 of 240 employees hired during a year had falsified their credentials? Round your answer to four decimal places.

In a binomial experiment find the probability of no more than 89 successes in 114 trials if . Round your answer to four decimal places.

Find the mode of the set of scores. 6, 11, 12, 6, 7, 5, 6, 5

Suppose an experiment has five possible outcomes for x: 1, 2, 3, 4, 5. The probability that each of these outcomes occurs is . Estimate the expected value of x for the experiment to two decimal places?

A die is rolled 2 times, and success is rolling a number greater than 3. Let x = number of success. Construct the binomial distribution that describes this experiment, and find the mean of this distribution.

Suppose a fair coin is tossed 12 times. What is the probability that exactly 10 heads will occur?

In a binomial experiment, find the probability 51 of 71 successes in trials if . Round your answer to four decimal places.

In a binomial experiment, find the probability of more than 43 successes in 110 trials if . Round your answer to four decimal places.

A coin is "loaded" so that the probability of tossing a head is . If it is tossed 50 times, what are the mean and the standard deviation of the number of heads that occur?

Suppose a population of scores x is normally distributed with and Use the standard normal distribution to find . Round your answer to four decimal places.

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 mode(s) of the scores. ​ 11, 12, 14, 10, 18, 12, 13, 14 ​