Introduction to Probability and Statistics, 14th Edition by William Mendenhall - Test Bank

Introduction to Probability and Statistics, 14th Edition by William Mendenhall – Test Bank

 

Instant Download – Complete Test Bank With Answers

 

 

Sample Questions Are Posted Below

 

MBB.IntroProb13.ch04sec7

 

TRUE/FALSE

 

1. Bayes’ Rule is a formula for revising an initial subjective (prior) probability value on the basis of results obtained by an empirical investigation and for, thus, obtaining a new (posterior) probability value.

 

ANS:  T                    PTS:   1

 

2. Given a set of events  that are mutually exclusive and exhaustive and an event A, the law of total probability states that P(A) can be expressed as .

 

ANS:  T                    PTS:   1

 

3. A false positive in screening tests is the event that the test is negative for a given condition, given that the person has the condition.

 

ANS:  F                    PTS:   1

 

4. A false negative in screening tests is the event that the test is positive for a given condition, given that the person does not have the condition.

 

ANS:  F                    PTS:   1

 

MULTIPLE CHOICE

 

1. A false negative in screening tests (e.g., Steroid testing of athletes) represents the event that:

 

a.	the test is negative for a given condition, given that the person does not have the condition
b.	the test is positive for a given condition, given that the person does not have the condition
c.	the test is negative for a given condition, given that the person has the condition
d.	the test is positive for a given condition, given that the person has the condition

 

 

ANS:  C                    PTS:   1

 

2. A false positive in screening (e.g., home pregnancy tests) represents the event that:

 

a.	the test is negative for a given condition, given that the person does not have the condition
b.	the test is positive for a given condition, given that the person does not have the condition
c.	the test is negative for a given condition, given that the person has the condition
d.	the test is positive for a given condition, given that the person has the condition

 

 

ANS:  B                    PTS:   1

 

3. Screening tests (e.g., AIDS testing) are evaluated on the probability of a false negative or a false positive, and both of these are:

 

a.	conditional probabilities
b.	probability of the intersection of two events
c.	probability of the union of two events
d.	marginal probabilities
e.	probability of dependent events

 

 

ANS:  A                    PTS:   1

 

PROBLEM

 

1. A sample is selected from one of two populations, S₁ and S₂, with probabilities P(S₁) = 0.80 and P(S₂) = 0.20. If the sample has been selected from S₁, the probability of observing an event A is P(A / S₁) = 0.15. Similarly, If the sample has been selected from S₂, the probability of observing A is P(A / S₂) = 0.25.

Round your answer to four decimal places, if necessary

 

1. If a sample is randomly selected from one of the two populations, what is the probability that event A occurs?

 

 

______________

 

If a sample is randomly selected and event A is observed, what is the probability that the sample was selected:

 

1. From population S₁?

 

 

______________

 

1. From population S₂?

 

 

______________

 

ANS:

1. 0.17; b. 0.7059; c. 0.2941

 

PTS:   1

 

2. Steve takes either a bus or the subway to go to work with probabilities 0.25 and 0.75, respectively. When he takes the bus, he is late 40% of the days. When he takes the subway, he is late 30% of the days. If Steve is late for work on a particular day, what is the probability that he took the bus?

 

 

______________

 

ANS:

0.3077

 

PTS:   1

 

3. Medical case histories indicate that different illnesses may produce identical symptom. Suppose a particular set of symptoms, which we will denote as event H, occurs only when any one of these illnesses: A, B, or C occurs. (For the sake of simplicity, we will assume that illnesses A, B, and C are mutually exclusive.) Studies show these probabilities of getting the three illnesses:

 

 

The probabilities of developing the symptoms H, given a specific illness, are:

 

 

Assuming that an ill person shows the symptoms H, what is the probability that the person has illness A?

Round your answer to four decimal places.

 

______________

 

ANS:

0.3669

 

PTS:   1