1) According to a large university, 35% 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 350 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?

(c) Interpret the standard deviation of the sampling distribution of.

(d) The admissions office finds that only 30% of the 350 graduates in the SRS had full time employment within one month of graduation.Assuming the university's claim that 35% will have employment is true, find the probability that 30% 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 35%?Justify.

2) A pediatrician has found that the heights of their patients follow a normal distribution with mean = 40 inches and standard deviation = 10.2 inches.Each day the doctor sees 15 patients, which can be considered a representative sample of the doctor's patients. Each of their heights is recorded and the mean is calculated.

(a) Calculate the mean and standard deviation of the sampling distribution ofor SRSs of size 12.

(b) Find the probability that the mean height is greater than 48.2 inches.