A normal population has a mean of $60 and standard deviation of $12. You select random samples of nine.

a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n = 9. With the small sample size, what condition is necessary to apply the central limit theorem?

b. What is the standard error of the sampling distribution of sample means?

c. What is the probability that a sample mean is greater than $63?

d. What is the probability that a sample mean is less than $56?

e. What is the probability that a sample mean is between $56 and $63?

f. What is the probability that the sampling error (x¯ − μ) would be $9 or more? That is, what is the probability that the estimate of the population mean is less than $51 or more than $69?