Age: Randomly Chosen?
A large community college district has 1500 teachers, of whom 50% are below 45 years and 50% are above 45 years of age. In this district, administrators are promoted from among the teachers. There are currently 80 administrators; 75% of these administrators are above 45 years of age.
a. If administrators are selected randomly from faculty, what is the approximate probability that the percentage of administrators above 45 years of age is 75% or more?
b. If administrators are selected randomly from the faculty, what is the approximate probability that the percentage of administrators below 45 years of age is 25% or less?
c. How are part a and part b related?
d. Do your answers suggest that it is reasonable to reject the claim that the administrators have been selected randomly from the teachers? Answer yes or no, and explain your answer.