1 The scores of students on the ACT college entrance examina

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 18 and 20?

D) What is the probability that the sample mean score falls within 2 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?

Solution