# Question

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 part a and part b related?

d. Do your 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.

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 part a and part b related?

d. Do your 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.

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