According to MSCI's 2014 Survey of Women on Boards, the percentage of women on U.S. S&P 1500 boards has increased marginally since 2001, and now stands at 16%, well below the values for France and Italy. This study also reports that 17% of U.S. S&P 1500 companies have three or more female board directors. (Data extracted from bit.ly/1MMiET1). Suppose you select a random sample of 200 U.S. S&P 1500 companies.

a. What is the probability that the sample will have between 14% and 20% U.S. S&P 1500 companies that have three or more female board directors?

b. The probability is 90% that the sample percentage of companies that have three or more female board directors will be contained within what symmetrical limits of the population percentage?

c. The probability is 95% that the sample percentage of companies that have three or more female board directors will be contained within what symmetrical limits of the population percentage?