# Statistics Problem Set: Pop Quizzes and Promotions

1. The female instructors at a large university recently lodged a complaint about the most recent round of promotions from assistant professor to associate professor. An analysis of the relationship between gender and promotion was undertaken which produced the joint probabilities in the following table.

Promoted Not Promoted

Female .03 .12

Male .17 .68

a) What is the rate of promotion among female assistant professors?

b) What is the rate of promotion among male assistant professors?

c) Is it reasonable to accuse the university of gender bias?

2. A student takes a pop quiz that consists of three true-false questions. Each question can be answered correctly (C) or incorrectly (I). Consider this to be a three-step process; i.e., answering the first question with a C or an I, answering the second question with a C or an I, and answering the third with a C or an I.

a) Identify each sample space outcome using the C and I designations.

b) What is the probability that the student gets all three questions correct?

c) What is the probability that the student gets exactly two questions correct?

d) What is the probability that the student gets at least two questions correct?

3. According to a Gallup Poll conducted March 5-7, 2001, 52% of American adults think that protecting the environment should be given priority over developing US energy supplies, 36% think developing energy supplies is more important, and 6% believe the two are equally important. The rest have no opinion. Suppose that a sample of 100 American adults is quizzed on the subject. What is the probability of the following events?

a) 50 or more think protecting the environment should be given priority

b) 30 or fewer think that developing energy supplies is more important

c) 5 or fewer have no opinion

4. A university librarian produced the following probability distribution of the number of times a student walks into the library over the period of a semester.

x 0 5 10 15 20 25 30 40 50 75 100

p(x) .22 .29 .12 .09 .08 .05 .04 .04 .03 .03 .01

Find the following probabilities:

a) P(X = 20)

b) P(X = 60)

c) P(X > 50)

d) P(X > 100)

5. The monthly returns on investment for Coca-Cola, Genentech, General Electric, General Motors, McDonald's and Motorola are stored in file Xr07-66 on the file below.

a) Compute the mean and variance of each stock.

b) If an investor wishes to maximize his expected return, which stock would you recommend?

c) If an investor wishes to minimize his risk, which stock would you recommend?

6. Because a continuous random variable can assume an infinite number of values, there is a probability that the random variable can assume a single value near one. Do you agree or disagree with this statement? Justify your response thanks

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#### Solution Preview

1. a) r = 0.03/0.15 = 0.2 = 20%

b) r = 0.17/0.85 = 0.2 = 20%

c) It is not reasonable to accuse the University of Gender Bias.

2. a) See attachment.

b) p = 0.125

c) p = 0.375

d) p = 0.5

3. a) Probability that 50 or more think ...