Could You Please find clear solution for following question? With best regards...

Question:

To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected.

a. Would you use the finite population correction factor in calculating the standard error of the mean? Explain.

b. If the population standard deviation is .2 years, compute the standard error both with and without the finite population correction factor. What is the rationale for ignoring the finite population correction factor whenever n/N=.05?

c. What is the probability that the sample mean age of the employees will be within 2 years of the population mean age?