chapter 6

Question 1

One die is thrown. What is the expected value of the number of dots on the top face of the die?

a) 1.0

b) 3.0

c) 3.5

d) 4.0

Answer 1

c) 3.5

Explanation
E[X]=1(1/6)+2(1/6)+3(1/6)+4(1/6)+5(1/6)+6(1/6)

Question 2

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

a) 9

b) 18

c) 1.732

d) 3

Correct

4.243

Answer 2

d) 3

Explanation
Binomial standard deviation = σ = √(npq) = √[(36)(.5)(.5)] = √9 = 3

Question 3

The internal auditor for your company believes that 10 percent of your 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?

a) .0433

b) .8660

c) .9567

d) .0319

Answer 3

a) 0.0433

Question 4

Which of the following is a valid probability value for a discrete random variable?

a) .2

b) 1.01

c) All of the choices are correct.

d) −.7

Answer 4

a) 2

Explanation
The probability of a discrete random variable can only be between 0 and +1.

Question 5

Which one of the following statements is not an assumption of the binomial distribution?

a) Each trial results in one of two mutually exclusive outcomes.

b) The probability of success remains constant from trial to trial.

c) Sampling is with replacement.

d) Trials are independent of each other.

e) The experiment consists of an identical trial.

Answer 5

c) Sampling is with replacement.

Explanation
All trials are independent and you do not replace once you have a success or failure.

Question 6

Which of the following is not a discrete random variable?

a) the number of criminals found in a five-mile radius of a neighborhood

b) the number of minutes required to run 1 mile

c) the number of times a light changes red in a 10-minute cycle

d) the number of defects in a sample selected from a population of 100 products

Answer 6

b) the number of minutes required to run 1 mile

Explanation
It could take someone infinite number of minutes to finish the 1 mile.

Question 7

Which of the following statements about the binomial distribution is not correct?

a) Trials are independent of each other.

b) The experiment consists of n identical trials.

c) Each trial results in a success or failure.

d) The probability of success remains constant from trial to trial.

e) The random variable of interest is continuous.

Answer 7

e) The random variable of interest is continuous.

Explanation
The random variable of interest needs to be discrete.

Question 8

The binomial distribution is characterized by situations that are analogous to

a) measuring the length of an item.

b) coin tossing.

c) drawing balls from an urn.

d) counting defects on an item.

Answer 8

b) coin tossing

Explanation
Binomial distributions assume a constant probability of success

Question 9

A total of 50 raffle tickets are sold for a contest to win a car. If you purchase one ticket, what are your odds against winning?

a) .01

b) 49 to 1

c) 50 to 1

d) .05

Answer 9

b) 49 to 1

Explanation
Probability of losing = 1 − probability of winning = 1 − 1/50 = 49/50.

Question 10

If x is a binomial random variable, then the standard deviation of x is given by

a) √npq.

b) npq.

c) (npq)2.

d) np.

Answer 10

a) √npq.

Explanation
Where n is the number of trials, p is the number of successes and q is the number of failures.