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.

Source: Data extracted from “The Tipping Point: Women on Boards and Financial Performance,” bit.ly/2pYDt9A.

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% U.S. companies that have three or more female board directors?

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