Question 1

If the probability that a certain couple will have a blue-eyed child is  , and they have 12 children, what is the probability that at least 1 child has blue eyes? ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

Suppose you live in a neighborhood with a few expensive homes and many modest homes. If you wanted to impress people with the neighborhood where you lived, which measure would you give as the "average" property value? ​

Accepted Answer

A) median 
B) minimum 
C) standard deviation 
D) mean 
E) range

Question 3

A variable x has a binomial distribution with probability of success 0.65 for each trial. For a total of 50 trials, what are the mean and the standard deviation of the distribution? ​

Accepted Answer

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

Question 4

An insurance company insures 100,000 cars in a certain area. The company has determined that on average, each year they will have to pay the following amounts for accidents in the area: ​
$100,000 with probability 0.0004
$50,000 with probability 0.001
$25,000 with probability 0.006
$5000 with probability 0.011
$1000 with probability 0.023
​
What is the company's expected payout per car each year?
​

Accepted Answer

A) $318.00 
B) $4163.00 
C) $4140.00 
D) $381.60 
E) $279.84

Question 5

In a binomial experiment find the probability of fewer than 13 successes in 110 trials if  . Round your answer to four decimal places. ​

Accepted Answer

A) 0.3156 
B) 0.5220 
C) 0.5025 
D) 0.6844 
E) 0.2993

Question 6

Find the median of the set of scores. ​
44, 86, 92, 58, 62, 70, 92
​

Accepted Answer

A) 58 
B) 72 
C) 92 
D) 70 
E) 48

Question 7

Suppose the probability of suicide among a certain age group is 0.006. If a randomly selected group of 150 Native Americans within this age group had no suicides, find the probability of this occurring by chance. Round your answer to four decimal places. ​

Accepted Answer

A) 0.3818 
B) 0.3595 
C) 0.4055 
D) 0.2221 
E) 0.2661

Question 8

Find the standard deviation of the sample data in the frequency table. Round your answer to two decimal places. ​  ​

Accepted Answer

A) 2.79 
B) 39.00 
C) 2.49 
D) 1.58 
E) 2.50

Question 9

Estimate the variance for the following probability distribution to two decimal places. ​  ​

Accepted Answer

A) 2.16 
B) 1.33 
C) 1.16 
D) 1.78 
E) 1.00

Question 10

The following table defines a discrete probability distribution. Find the expected value of the distribution. ​  ​

Accepted Answer

A) E(x)=  
B) E(x)=  
C) E(x)=  
D) E(x)=10 
E) E(x)=1

Question 11

A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 22 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has gas mileage less than 21 mpg. Round your answer to four decimal places. ​

Accepted Answer

A) 0.4013 
B) 0.9013 
C) 0.0987 
D) 0.5987 
E) 0.1974

Question 12

Find the mean of the following data. Round your answer to the nearest integer. ​
Interval
Frequency  4  2  4  6  9

Accepted Answer

A) 24 
B) 64 
C) 41 
D) 60 
E) 102

Question 13

Suppose that the ratio of boys born to girls born is 120 to 100, what is the probability that out of 2500 babies born in Santa Clara, 1180 will be girls? Round your answer to four decimal places. ​

Accepted Answer

A) 0.9966 
B) 0.2044 
C) 0.4721 
D) 0.0034 
E) 0.2460

Question 14

Suppose a television show rating of 6.4 means that 6.4% of the 110 million TV households watched the show. If a sample of 123 local TV households were queried, what is the probability that more than 9 would have watched the show? Round your answer to four decimal places. ​

Accepted Answer

A) ​0.3604 
B) ​0.2743 
C) ​0.7257 
D) ​0.5254 
E) ​0.4219

Question 15

True or False: Probabilities from a binomial probability distribution with  trials and with the probability of success on each trial equal to  can be approximated by using a normal distribution.​ ​

Accepted Answer

A) ​false 
B) ​true

Question 16

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) 0.1915 
B) 0.5000 
C) 0.8085 
D) 0.0958 
E) 0.6915

Question 17

A candidate must decide whether he should spend his time and money on TV commercials or making personal appearances. His staff determines that by using TV he can reach 110,000 people with probability 0.06, 55,000 people with probability 0.39, and 30,000 people with probability 0.55; by making personal appearances he can reach 80,000 people with probability 0.04, 60,000 people with probability 0.36, and 25,000 people with probability 0.6. In the following table, x represents the number of people reached by each choice. In each case, find the expected value of x to decide which method, if either, will reach more people. ​  ​

Accepted Answer

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

Question 18

Suppose that 8% of the patients who have a certain disease will die from it. If 80 people have the disease, how many would we expect to die from it, and what is the standard deviation of the number of deaths that could occur? Round any estimated quantities to two decimal places. ​

Accepted Answer

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

Question 19

A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 40 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has gas mileage greater than 50 mpg. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Accepted Answer

A) ​0.9938 
B) ​0.0062 
C) ​0.9907 
D) ​0.4938 
E) ​0.0169

Question 20

Find the range of the set of numbers given. ​
2, 9, 4, 2, 7, 3, 8
​

Accepted Answer

A) 4 
B) 2 
C) 7 
D) 5 
E) 8

Exam 9: Further Topics in Probability; Data Description

If the probability that a certain couple will have a blue-eyed child is , and they have 12 children, what is the probability that at least 1 child has blue eyes?

Suppose you live in a neighborhood with a few expensive homes and many modest homes. If you wanted to impress people with the neighborhood where you lived, which measure would you give as the "average" property value?

A variable x has a binomial distribution with probability of success 0.65 for each trial. For a total of 50 trials, what are the mean and the standard deviation of the distribution?

In a binomial experiment find the probability of fewer than 13 successes in 110 trials if . Round your answer to four decimal places.

Find the median of the set of scores. 44, 86, 92, 58, 62, 70, 92

Suppose the probability of suicide among a certain age group is 0.006. If a randomly selected group of 150 Native Americans within this age group had no suicides, find the probability of this occurring by chance. Round your answer to four decimal places.

Find the standard deviation of the sample data in the frequency table. Round your answer to two decimal places.

Estimate the variance for the following probability distribution to two decimal places.

The following table defines a discrete probability distribution. Find the expected value of the distribution.

A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 22 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has gas mileage less than 21 mpg. Round your answer to four decimal places.

Find the mean of the following data. Round your answer to the nearest integer. Interval Frequency 4 2 4 6 9

Suppose that the ratio of boys born to girls born is 120 to 100, what is the probability that out of 2500 babies born in Santa Clara, 1180 will be girls? Round your answer to four decimal places.

Suppose a television show rating of 6.4 means that 6.4% of the 110 million TV households watched the show. If a sample of 123 local TV households were queried, what is the probability that more than 9 would have watched the show? Round your answer to four decimal places.

True or False: Probabilities from a binomial probability distribution with trials and with the probability of success on each trial equal to can be approximated by using a normal distribution.

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.

Suppose that 8% of the patients who have a certain disease will die from it. If 80 people have the disease, how many would we expect to die from it, and what is the standard deviation of the number of deaths that could occur? Round any estimated quantities to two decimal places.

Find the range of the set of numbers given. 2, 9, 4, 2, 7, 3, 8