The scores of individual students on the American College Te

The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the sampling distribution of the sample mean score for a random sample of 36 students?

a. Neither Normal nor nonNormal—it depends on the particular 36 students selected

b. Approximately Normal, but the approximation is poor

c. Approximately Normal, and the approximation is good

d. Exactly Normal

please explain

Solution

d. Exactly normal

When the population is normal, the sample size taken out of it will also have a normal distribution.