The scores of individual students on the American College Te

The scores of individual students on the American College Testing (ACT) Program Compos- ite College Entrance Examination have a Normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores.

(a) What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?

(b) What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?

(c) What is the sampling distribution of the sample mean score for a random sample of 36 students?

Solution

a. sample mean =18.6

b. sample standard deviation = standard deviation / root n =6/6= 1

c. Normal distribution(since we have a large sample) mean 18.6 and standard deviation 1