A random sample is drawn from a normally distributed population with mean = 12 and standard deviation = 1.5. a. What is the

A random sample is drawn from a normally distributed population with mean μ = 12 and standard deviation σ = 1.5.

a. What is the expected value and the standard error of the sampling distribution of the sample mean with n = 20 and n = 40.

b. Can you conclude that the sampling distribution of the sample mean is normally distributed for both sample sizes? Explain.

c. If the sampling distribution of the sample mean is normally distributed with n = 20, then calculate the probability that the sample mean is less than 12.5.

d. If the sampling distribution of the sample mean is normally distributed with n = 40, then calculate the probability that the sample mean is less than 12.5.