A large community college district has 1000

1000 teachers, of whom 50

50% are men and 50

50% are women. In thisdistrict, administrators are promoted from among the teachers. There are currently 20

20 administrators, and 75

75% of these administrators are men. Complete parts(a) through(d) below.

a. If administrators are selected randomly from thefaculty, what is the approximate probability that the percentage of male administrators will be 75

75% ormore?

. 013

.013 (Round to three decimal places asneeded.)

b. If administrators are selected randomly from thefaculty, what is the approximate probability that the percentage of female administrators will be 25

25% orless?

. 013

.013 (Round to three decimal places asneeded.)

c. How are part(a) and part(b) related?

A.

These two questions are identical because the population proportions of men and women are equal. The probabilities of selecting67% or more males and selecting33% or less females would also be equal.

B.

Selecting 75

75% or more males is the same as selecting 25

25% or less females. The probabilities are complements.

C.

Selecting 75

75% or more males is the same as selecting 25

25% or less females. These two questions are identical.

Your answer is correct.

D.

The parts are only related because the probabilities are coincidentally complements.

d. Does your answers suggest that it is reasonable to believe the claim that the administrators have been selected randomly from theteachers? Let a probability less than 5% suggest an unreasonable claim.

It is not to believe the claim that the administrators have been selected randomly since the probability that the percentage of male administrators will be 75% or more is low;

there is a ___% chance it would occur by chance.

(Round to one decimal place asneeded.)