5.95 Summer employment of college students. Suppose (as is roughly true) that 88% of college men and 82% of college women were employed last summer. A sample survey interviews SRSs of 400 college men and 400 college women. The two samples are of course independent.

1. (a) What is the approximate distribution of the proportion of women who worked last summer? What is the approximate distribution of the proportion of men who worked?

2. (b) The survey wants to compare men and women. What is the approximate distribution of the difference in the proportions who worked, ? Explain the reasoning behind your answer.

3. (c) What is the probability that in the sample a higher proportion of women than men worked last summer?