A random sample of size n = 100 is taken from a population of size N = 2,500 with mean = -45 and variance 2 = 81.

a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of the sample mean.

b. What is the probability that the sample mean is between -47 and -43?

c. What is the probability that the sample mean is greater than -44