1. A standardized test given to all new applicants is normally distributed with a mean of 75 and a standard deviation of 15. A random sample of 30 applicants is selected for further study.

A) What is the shape, mean(expected value) and standard deviation of the sampling distribution of the sample mean for samples of size 30?

B) What is the probability that the sample mean will be larger than 80?

C) What is the probability that the sample mean will fall within 7 points of the population mean?

D) What is the probability that the sample mean will be less than 69?

2. Assume that the population proportion of adults who smoke cigarettes is 0.39. A random sample of 300 adults is to be selected to test this claim.

A) What is the shape, mean, and standard deviation of the sampling distribution of the sample proportion for samples of 300?

B) What is the probability that the sample proportion will be less than 0.45?

C) What is the probability that the sample proportion will fall within 4 percentage points(+/- 0.04) of the population proportion?