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.

(a) What is the approximate distribution of the proportion p_F of women who worked last summer? (Round your standard deviation to four decimal places.)

What is the approximate distribution of the proportion p_M of men who worked? (Round your standard deviation to four decimal places.)

(b) The survey wants to compare men and women. What is the approximate distribution of the difference in the proportions who worked, p_M p_F?

(c) What is the probability that in the sample a higher proportion of women than men worked last summer? (Round your answer to four decimal places.)