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 20 administrators, and 65% of these administrators are men. Complete parts (a) through (d) below. a. If administrators are selected randomly from the faculty, what is the approximate probability that the percentage of male administrators will be 65% or more? 1.34 (Round to three decimal places as needed.) b. If administrators are selected randomly from the faculty, what is the approximate probability that the percentage of female administrators will be 35% or less? 0.09 (Round to three decimal places as needed.) c. How are part (a) and part (b) related? O A. These two questions are identical because the population proportions of men and women are equal. The probabilities of selecting 67% or more males and selecting 33% or less females would also be equal. OB. Selecting 65 % more males is the same as selecting 35% or less females. The probabilities are complements. Oc. Selecting 65% or more males is the same as selecting 35% or less females. These two questions are identical. OD. The parts are only related because the probabilities are coincidentally complements. d. Do your answers suggest that it is reasonable to believe the claim that the administrators have been selected randomly from the teachers? Let a probability less than 10% suggest an unreasonable claim. It is V to believe the claim that the administrators have been selected randomly since the probability that the percentage of male administrators will be 65% or more is V there is a% chance it would occur (Round to one decimal place as needed.)