Referring to Problem 7.18, the same survey reported that 20.9% of German companies have women directors and 80% have three or more women on the board.

If you select a random sample of 200 German companies,

a. What is the probability that the sample will have between 70% and 78% 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?

Problem 7.18

According to a survey in December 2018 of Women on Boards, women hold 21.7% of director seats on U.S. corporate boards. This study also reports that 39.2% 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?