Question 1

Your company's internal auditor believes that 10% of the company's invoices contain errors.To check this theory,20 invoices are randomly selected and 5 are found to have errors. Would you accept or reject the claim?
A)Accept the auditor's claim
B)Reject the auditor's claim

Accepted Answer

Reject claim because P < .05

Question 2

According to data from the state blood program,40% of all individuals have group A blood.If six (6)individuals give blood,find the probability Find the mean number of individuals having group A blood.
A)1.2
B)1.55
C)1.44
D)2.4

Accepted Answer

The mean number of individuals having group A blood can be found using the formula for the mean of a binomial distribution: mean = n * p, where n is the number of trials (6 individuals) and p is the probability of success (0.4 for group A blood). Thus, mean = 6 * 0.4 = 2.4.

Question 3

According to data from the state blood program,40% of all individuals have group A blood.If six (6)individuals give blood,find the probability Exactly three of the individuals has group A blood?
A).4000
B).2765
C).5875
D).0041

Accepted Answer

The probability of an individual having group A blood is 0.4. The probability of an individual not having group A blood is 0.6. The probability of exactly three individuals having group A blood out of six is given by the binomial distribution:P(X = 3) = (6 choose 3) * (0.4)^3 * (0.6)^3 = 0.2765Therefore, the probability of exactly three of the individuals having group A blood is 0.2765, which is choice B.

Question 4

Your company's internal auditor believes that 10% of the company's 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 written,five or more would contain errors if the theory is valid?
A).0433
B).0319
C).9567
D).8660

Accepted Answer

P(x F1F1F1S1F1F1F10 5)= (.0319)+ (.0089)+ (.0020)+ (.0004)+ (0001)= .0433

Question 5

According to data from the state blood program,40% of all individuals have group A blood.If six (6)individuals give blood,find the probability Suppose that of the six randomly selected individuals,3 have group A blood.Would you believe the data from the state blood program?
A)Yes,probability is > .05
B)Yes,probability is < .05
C)No

Accepted Answer

The probability of exactly 3 out of 6 individuals having group A blood can be calculated using the binomial probability formula. With a probability greater than 0.05, the data from the state blood program is believable.

Question 6

A lawyer believes that the probability is .3 that she can win a discrimination suit.If she wins the case she will make $40,000,but if she loses she gets nothing.Assume that she has to spend $5000 preparing the case.What is her expected gain?
A)$35,000
B)$7,000
C)$10,500
D)$9,000

Accepted Answer

= (.7)(-5000)+ (.3)(35000)= 7000

Question 7

According to data from the state blood program,40% of all individuals have group A blood.If six (6)individuals give blood,find the probability At least 3 of the individuals have group A blood.
A).8208
B).5443
C).4557
D).1792

Accepted Answer

P(x F1F1F1S1F1F1F10 3)= P(x = 3)+ p(x = 4)+ p(x = 5)+ p(x = 6)= .4557

Question 8

A car wash loses $30 on rainy days and makes $120 on days when it does not rain.If the probability of rain is 0.15,calculate the car wash's expected profit.
A)$90
B)$76.50
C)$106.50
D)$97.50

Accepted Answer

= (-30)(.15)+ (120)(.85)= -4.50 + 102 = 97.50

Question 9

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired.Historically,the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day.For the first five troubles reported on a given day,what is the probability that: All five will be repaired on the same day?
A).0010
B).6328
C).9990
D).2373

Accepted Answer

P(x = 5)= .2373

Question 10

A pharmaceutical company has determined that if a new cholesterol-reducing drug is manufactured (introduced to the market),the following probability distribution will describe this drug's contribution to the company's profits during the next six months.  The company management has decided to market this product if the expected contribution to profit for the next six months is more than $90,000.Based on the information given above,should the company begin manufacturing the new drug?
A)Yes,begin manufacturing
B)No,don't begin manufacturing

Accepted Answer

(79,000 < 90,000)= .2(-30,000)+ .5(50,000)+ .3(200,000)= 79,000

Question 11

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 standard deviation for this distribution?
A)1.5
B)1.22
C)0.75
D)0.87

Accepted Answer

The distribution of X is a binomial distribution with parameters n=3 and p=0.5 (since the coin is fair). The standard deviation of a binomial distribution is given by the formula:
SD = sqrt(n*p*(1-p))
Substituting n=3 and p=0.5, we get:
SD = sqrt(3*0.5*(1-0.5)) = sqrt(0.75) = 0.87
Therefore, the answer is D) 0.87.

Question 12

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day.Of the eight,what is the average number you expect to be delivered the next day?
A)3.6
B)4.0
C)7.2
D)2.7

Accepted Answer

= np = (8)(.9)= 7.2

Question 13

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day when there are 8 local letters mailed .What is the probability that the number of delivered will be within 2 standard deviations of the mean?
A).9950
B).9619
C).8131
D).9996

Accepted Answer

P(7.2 F1F1F1S1F1F1F10 2(.85))= p(7.2 F1F1F1S1F1F1F10 1.7)= P(5.5 F1F1F1S1F1F1F10 x F1F1F1S1F1F1F10 8)= P(6 F1F1F1S1F1F1F10 x F1F1F1S1F1F1F10 8)= (.4305)+ (.3826)+ (.1488)= .9619

Question 14

According to data from the state blood program,40% of all individuals have group A blood.If six (6)individuals give blood,find the probability None of the individuals has group A blood?
A).0041
B).0410
C).4000
D).0467

Accepted Answer

The probability of one individual not having group A blood is 1-0.4=0.6. To find the probability of none of the six individuals having group A blood, we multiply the probabilities of each individual not having group A blood together: 0.6*0.6*0.6*0.6*0.6*0.6=0.0466. Rounded to four decimal places, this is 0.0467. Therefore, the correct answer is D) 0.0467.

Question 15

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day.Calculate the standard deviation of the number delivered when 8 local letters are mailed.
A).85
B).72
C)2.68
D)2.83

Accepted Answer

F1F1F1S1F1F1F10 = = = = .85

Question 16

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). 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?
A)$3
B)$2
C)$6
D)$9

Accepted Answer

The expected value of X (number of heads) when tossing a fair coin three times is 1.5. Since you earn $2 for each head, the expected winnings are 1.5 * $2 = $3.

Question 17

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired.Historically,the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day.For the first five troubles reported on a given day,what is the probability that: At least 3 troubles will be repaired on the same day.
A).1035
B).0376
C).9624
D).8965

Accepted Answer

P(x F1F1F1S1F1F1F10 3)= 1 - (P F1F1F1S1F1F1F10 2)= .8965

Question 18

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day.If you mail eight local letters,what is the probability that all of them will be delivered the next day.
A)1.0
B).4305
C).8131
D).5695

Accepted Answer

P(x = 8)= .4305

Question 19

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired.Historically,the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day.For the first five troubles reported on a given day,what is the probability that: Find the mean number of troubles repaired on the same day.
A)3.75
B)0.94
C)1.94
D)2.50

Accepted Answer

= np = (5)(.75)= 3.75

Question 20

An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired.Historically,the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day.For the first five troubles reported on a given day,what is the probability that: Fewer than two troubles will be repaired on the same day?
A).6328
B).0010
C).0156
D).0146

Accepted Answer

P(x < 2)= P(x = 0)+ P(x = 1)= .0156

Quiz 5: Discrete Random Variables

Your company's internal auditor believes that 10% of the company's invoices contain errors.To check this theory,20 invoices are randomly selected and 5 are found to have errors. Would you accept or reject the claim?

According to data from the state blood program,40% of all individuals have group A blood.If six (6) individuals give blood,find the probability Find the mean number of individuals having group A blood.

According to data from the state blood program,40% of all individuals have group A blood.If six (6) individuals give blood,find the probability Exactly three of the individuals has group A blood?

Your company's internal auditor believes that 10% of the company's 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 written,five or more would contain errors if the theory is valid?

According to data from the state blood program,40% of all individuals have group A blood.If six (6) individuals give blood,find the probability Suppose that of the six randomly selected individuals,3 have group A blood.Would you believe the data from the state blood program?

A lawyer believes that the probability is .3 that she can win a discrimination suit.If she wins the case she will make $40,000,but if she loses she gets nothing.Assume that she has to spend $5000 preparing the case.What is her expected gain?

According to data from the state blood program,40% of all individuals have group A blood.If six (6) individuals give blood,find the probability At least 3 of the individuals have group A blood.

A car wash loses $30 on rainy days and makes $120 on days when it does not rain.If the probability of rain is 0.15,calculate the car wash's expected profit.

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 standard deviation for this distribution?

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day.Of the eight,what is the average number you expect to be delivered the next day?

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day when there are 8 local letters mailed .What is the probability that the number of delivered will be within 2 standard deviations of the mean?

According to data from the state blood program,40% of all individuals have group A blood.If six (6) individuals give blood,find the probability None of the individuals has group A blood?

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

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads) . 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?

The Post Office has established a record in a major Midwestern city for delivering 90% of its local mail the next working day.If you mail eight local letters,what is the probability that all of them will be delivered the next day.