According to the MSCI 2016 Survey of Women on Boards, women hold 20% of director seats on U.S. corporate boards. This study also reports that 34% of U.S. companies have three or more female board directors.

If you select a random sample of 200 U.S. companies,

a. What is the probability that the sample will have between 30% and 38% 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?