According to Catalyst, a New York-based women's advocacy and research group, 12% of all corporate officers at the 500 largest U.S. corporations in 1999 were women, compared to 8% in 1995. (Atlanta Journal Constitution, Nov. 12, 1999).

a. According to Catalyst's data, in a sample of 1,000 corporate officers at the 500 largest U.S. firms, how many would you expect to be women?

b. If eight corporate officers were randomly selected from the 500 largest U.S. firms, what is the probability that none would be women? That half would be women?

c. What assumptions did you have to make in order to answer part b using the binomial distribution?