A random sample is drawn from a normally distributed population with mean μ = 12 and standard deviation σ = 1.5. [You may find it useful to reference the z table.].


a. What is the expected value and the standard error of the sampling distribution of the sample mean with n = 20 and n = 40. (Round the standard error to 3 decimal places.)

b. 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. (If appropriate, round final answer to 4 decimal places.




c. 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. (If appropriate, round final answer to 4 decimal places.)