A large community college district has 1000 teachers, of whom 50% are men and 50% are women. In this district administrators are promoted from among the teachers. There are currently 50 administrators, and 70% of these administrators are men.

A. If administrators are selected randomly from the faculty, what is the approximate probability that the percentage of male administrators will be 70% or more?

B. If administrators are selected randomly from the faculty, what is the approximate probability that the percentage of female administrators will be 30% or less?

C. How are par a and part b related?

D. Do you answers suggest that it is reasonable to believe the claim that the administrators have been selected randomly from the teachers? Answer yes or no and explain your answer.