Module 1, Ch 2, Exercises

Student 041201

Module 1, Ch 2, Exercises

2-14

A student taking Management Science 301 at East Haven University will receive one of the five possible grades fro the course: A, B, C, D, or F. The distribution of the grades over the past two years is as follows:

Grade Number of Students

A 80

B 75

C 90

D 30

F 25

Total 300

If this past distribution is a good indicator of future grades, what is the probability of a student receiving a C in the course?

2-16

An urn contains 8 red chips, 10 green chips, and 2 white chips. A chip is drawn and replaced, and then a second chip is drawn. What is the probability of

(a) a white chip on the first draw?

(b) a white chip on the first draw and a red on the second?

(c) two green chips being drawn?

(d) a red chip on the second, given that a white chip was drawn on the first?

2-19

The Springfield Kings, a professional basketball team, has won 12 of its last 20 games and is expected to continue winning at the same percentage rate. The team’s ticket manager is anxious to attract a large crowd to tomorrow’s game but believes that depends on how well the Kings perform tonight against the Galveston Comets. He assesses the probability of drawing a large crowd to be 0.90 should the team win tonight. What is the probability that the team wins tonight and there will be a large crowd at tomorrow’s game?

2-23

Ace Machine Works estimates that the probability its lathe tool is properly adjusted is 0.8. When the lathe is properly adjusted, there is a 0.9 probability that the parts produced pass inspection. If the lathe is out of adjustment, however, the probability of a good part being produced is only 0.2. A part randomly chosen is inspected and found to be acceptable. At this point, what is the posterior probability that the lathe tool is properly adjusted?

2-26

The Northside Rifle team has two markspersons, Dick and Sally. Dick hits a bull’s-eye 90% of the time and Sally hits a bull’s-eye 95% of the time.

(a) What is the probability that either Dick or Sally or both will hit the bull’s-eye if each takes one shot?

(b) What is the probability that Dick and Sally will hit both the bull’s-eye?

(c) Did you make any assumptions in answering the preceding questions? If you answered yes, do you think you are justified in making the assumption(s)?

2-31

What are the expected value and variance of the following probability distribution?

RANDOM VARIABLE X PROBABILITY

1 0.05

2 0.05

3 0.10

4 0.10

5 0.15

6 0.15

7 0.25

8 0.15

2-34

If

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