ccording to a large university, 32% of their graduating class will have full time employment within

one month after graduation. The admissions office wants to investigate this claim. They contact

an SRS of 300 of the previous semester's graduates. Let

= the proportion of graduates in this

sample who had full time employment within one month of graduation.

(a) What is the shape of the sampling distribution of ? Justify.

(b) What are the mean and standard deviation of the sampling distribution of ?

(d) The admissions office finds that only 29% of the 300 graduates in the SRS had full time

employment within one month of graduation. Assuming the university's claim that 32% will have

employment is true, find the probability that 29% or less of a sample of 300 have full time

employment.

(e) Does the admissions office have convincing evidence that the proportion of graduates who have

full time employment within one month of graduating is actually lower than 32%? Justify.