Question 1

If the probability distribution of X is:  What is the variance of X?

Accepted Answer

A) 1.0 
B) 5.0 
C) 2.25 
D) 2.24

Question 2

The probability that a given computer chip will fail is 0.02.Find the probability that of 5 delivered chips,exactly 2 will fail.

Accepted Answer

A) .9039 
B) .0922 
C) .0038 
D) .0000

Question 3

The hypergeometric probability distribution can be approximated by the Poisson distribution.

Accepted Answer

A) True 
 B)False

Question 4

A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6)outcomes?

Accepted Answer

A) 18 
B) 9 
C) 5 
D) 3 
E) 1.732

Question 5

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the variance of X.

Accepted Answer

A) 3 
B) 9 
C) 1.5 
D) 1.7

Question 6

The internal auditor for your company believes that 10 percent of their invoices contain errors.To check this theory,20 invoices are randomly selected,and 5 are found to have errors.What is the probability that of the 20 invoices selected,5 or more would contain errors if the theory is valid?

Accepted Answer

A) .0433 
B) .0319 
C) .9567 
D) .8660

Question 7

Historical data for a local steel manufacturing company show that the average number of defects per standard sheet of steel is 2.In addition,the number of defects per unit is distributed according to a Poisson distribution.A batch has just been completed.What is the probability that the first three units manufactured in this batch will contain at least a total of 4 defects?

Accepted Answer

A) .8488 
B) .7149 
C) .1512 
D) .2851

Question 8

The property of expected values says if a and b are constants,and if x and y are random variables,then μ(ax + by) = aμx + bμy + 2ab.

Accepted Answer

A) True 
 B)False

Question 9

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

Accepted Answer

A) $3 
B) $2 
C) $6 
D) $9

Question 10

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads).What is the variance for this distribution?

Accepted Answer

A) 1.5 
B) 1.22 
C) 0.75 
D) 0.87

Question 11

According to data from the state blood program,40 percent of all individuals have group A blood.If six individuals give blood,find the mean number of individuals having group A blood.

Accepted Answer

A) 1.2 
B) 1.55 
C) 1.44 
D) 2.4

Question 12

Given that x is the yearly proportional return for stock G and y is the yearly proportional return for stock H,μ_x = .16,μ_y = .07,σ_x = .11,σ_y = .11,and σ_xy² = .0321.Find the mean and standard deviation of the portfolio return: P = .45x + .55y.

Accepted Answer

The answer of Given that x is the yearly proportional...

Question 13

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that exactly 3 support increased spending on environmental issues.

Accepted Answer

A) .0330 
B) .1318 
C) .7844 
D) .9624

Question 14

The variable Employment Status,which can take either the value 1 for Employed and 0 for Unemployed,is an example of a _____________ random variable.

Accepted Answer

A) Poisson 
B) Discrete 
C) Hypergeometric 
D) Continuous

Question 15

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day.Calculate the standard deviation of the number delivered when 8 local letters are mailed.

Accepted Answer

A) .85 
B) .72 
C) 2.68 
D) 2.83

Question 16

Using the following probability distribution table of the random variable x,what is the probability of x = 3?

Accepted Answer

A) 3/15 
B) 5/15 
C) 1/15 
D) 2/15

Question 17

For a random variable X,the mean value of the squared deviations of its values from their expected value is called its ____________.

Accepted Answer

A) Standard deviation 
B) Mean 
C) Probability 
D) Variance

Question 18

Which of the following is not a discrete random variable?

Accepted Answer

A) The number of times a light changes red in a 10-minute cycle. 
B) The number of minutes required to run 1 mile. 
C) The number of defects in a sample selected from a population of 100 products. 
D) The number of criminals found in a five-mile radius of a neighborhood.

Question 19

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number).

Accepted Answer

A) 56 
B) 35 
C) 29 
D) 25

Question 20

Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the standard deviation of X.

Accepted Answer

A) 2 
B) 4 
C) 16 
D) 1.5

Exam 5: Discrete Random Variables

If the probability distribution of X is: What is the variance of X?

The probability that a given computer chip will fail is 0.02.Find the probability that of 5 delivered chips,exactly 2 will fail.

The hypergeometric probability distribution can be approximated by the Poisson distribution.

A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6) outcomes?

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the variance of X.

The internal auditor for your company believes that 10 percent of their invoices contain errors.To check this theory,20 invoices are randomly selected,and 5 are found to have errors.What is the probability that of the 20 invoices selected,5 or more would contain errors if the theory is valid?

The property of expected values says if a and b are constants,and if x and y are random variables,then μ_{(ax + by)} = aμ_x + bμ_y + 2ab.

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads) .What is the variance for this distribution?

According to data from the state blood program,40 percent of all individuals have group A blood.If six individuals give blood,find the mean number of individuals having group A blood.

Given that x is the yearly proportional return for stock G and y is the yearly proportional return for stock H,μ_x = .16,μ_y = .07,σ_x = .11,σ_y = .11,and σ_xy² = .0321.Find the mean and standard deviation of the portfolio return: P = .45x + .55y.

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that exactly 3 support increased spending on environmental issues.

The variable Employment Status,which can take either the value 1 for Employed and 0 for Unemployed,is an example of a _____________ random variable.

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day.Calculate the standard deviation of the number delivered when 8 local letters are mailed.

Using the following probability distribution table of the random variable x,what is the probability of x = 3?

For a random variable X,the mean value of the squared deviations of its values from their expected value is called its ____________.

Which of the following is not a discrete random variable?

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number) .

Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the standard deviation of X.

Exam 5: Discrete Random Variables

If the probability distribution of X is: What is the variance of X?

The probability that a given computer chip will fail is 0.02.Find the probability that of 5 delivered chips,exactly 2 will fail.

The hypergeometric probability distribution can be approximated by the Poisson distribution.

A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6) outcomes?

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the variance of X.

The internal auditor for your company believes that 10 percent of their invoices contain errors.To check this theory,20 invoices are randomly selected,and 5 are found to have errors.What is the probability that of the 20 invoices selected,5 or more would contain errors if the theory is valid?

The property of expected values says if a and b are constants,and if x and y are random variables,then μ(ax + by) = aμx + bμy + 2ab.

If you were asked to play a game in which you tossed a fair coin three times and were given $2 for every head you threw,how much would you expect to win on average?

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads) .What is the variance for this distribution?

According to data from the state blood program,40 percent of all individuals have group A blood.If six individuals give blood,find the mean number of individuals having group A blood.

Given that x is the yearly proportional return for stock G and y is the yearly proportional return for stock H,μx = .16,μy = .07,σx = .11,σy = .11,and σxy2 = .0321.Find the mean and standard deviation of the portfolio return: P = .45x + .55y.

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that exactly 3 support increased spending on environmental issues.

The variable Employment Status,which can take either the value 1 for Employed and 0 for Unemployed,is an example of a _____________ random variable.

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day.Calculate the standard deviation of the number delivered when 8 local letters are mailed.

Using the following probability distribution table of the random variable x,what is the probability of x = 3?

For a random variable X,the mean value of the squared deviations of its values from their expected value is called its ____________.

Which of the following is not a discrete random variable?

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number) .

Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the standard deviation of X.

The property of expected values says if a and b are constants,and if x and y are random variables,then μ_{(ax + by)} = aμ_x + bμ_y + 2ab.

Given that x is the yearly proportional return for stock G and y is the yearly proportional return for stock H,μ_x = .16,μ_y = .07,σ_x = .11,σ_y = .11,and σ_xy² = .0321.Find the mean and standard deviation of the portfolio return: P = .45x + .55y.