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 10% of all disk drives produced on an assembly line are defective, what is the probability there will be exactly one defect in a random sample of 5 of these? What is the probability that there will be no defects in a random sample of 5?

2-37

An industrial oven used to cure sand cores for a factory manufacturing engine blocks for small cars is able to maintain fairly constant temperatures. The temperature range of the oven follows a normal distribution with a mean of 450 degrees F and a standard deviation of 25 degrees F. Leslie Larsen, president of the factory, is concerned about the large number of defective cores that have been produced in the past several months. If the oven gets hotter than 475 degrees F. the core is defective. What is the probability that the oven will cause a core to be defective? What is the probability that the temperature of the oven will range from 460 degrees to 470 degrees F?

2-39

Susan Williams

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