1. The scores of students on the ACT college entrance examination in a recent year had a normal distribution with a mean of 18.6 and a standard deviation of 5.9. A simple random sample of 60 students who took the the exam is selected for study.
A) What are the shape, mean(expected value), and standard deviation of the sampling distribution of the sample mean for samples of size 60?
B) What is the probability that the sample mean score will be 20 or higher?
C) What is the probability that the sample mean score will be between 20 and 30?
D) What is the probability that the sample mean score falls within 3 points of the population mean score?
E) What value does the sample mean score have to be in order for it to be in the top 5% of the sampling distribution?
2. Last year, a national opinion poll found that 43% of all Americans agree that parents should be given vouchers good for education at any public or private school of their choice. Assume that in fact the population proportion is 0.43. This year, a random sample of 350 is to be selected and asked the same question.
A) What are the shape, mean(expected value), 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 fall within 0.03 of the population proportion?
3. Redo part B) of problem #2, but assume that the sample size is 700. By how much does your answer change and WHY?