Question: A study of women in corporate leadership was conducted by Catalyst, a New York research organization. The study concluded that slightly more than 15% of corporate officers at Fortune 500 companies are women (C. Hymowitz, Women Put Noses to the Grindstone, and Miss Opportunities, The Wall Street Journal, February 3, 2004, p. B1). Suppose that you select a random sample of 200 corporate officers, and the true proportion held by women is 0.15.
a. What is the probability that in the sample, less than 15% of the corporate officers will be women?
b. What is the probability that in the sample, between 13% and 17% of the corporate officers will be women?
c. What is the probability that in the sample, between 10% and 20% of the corporate officers will be women?
d. If a sample of 100 is taken, how does this change your answers to (a) through (c)?