A normal population has a mean of $75 and standard deviation of $5. You select random samples of 40.

a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n = 40. 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 less than $74?

d. What is the probability that a sample mean is between $74 and $76?

e. What is the probability that a sample mean is between $76 and $77?

f. What is the probability that the sampling error (X̅ − μ) would be $1.50 or less?