Sampling distribution

1. The SAT test scores have an average value of 1200 with a standard deviation of 100. A random sample of 45 scores is selected for study.

A) What is the shape, mean(expected value) and standard deviation of the sampling distribution of the sample mean for samples of size 45?

B) What is the probability that the sample mean will be larger than 1240?

C) What is the probability that the sample mean will fall within 25 points of the population mean?

D) What is the probability that the sample mean will be less than 1170?

2. Assume that the population proportion of adults having a college degree is 0.38. A random sample of 350 adults is to be selected to test this claim.

A) What are the shape, mean, and standard deviation of the sampling distribution of the sample proportion for samples of 350?

B) What is the probability that the sample proportion will be less than 0.40?

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