A random sam ple of size n = 100 is taken from a population of size N = 2,500 with m ean μ = —45 and variance σ2 = 81.

a. Is it necessary to apply th e finite population correction factor? Explain. Calculate the expected value and the standard deviation of th e sam ple m ean.

b. W hat is th e probability th a t th e sam ple m ean is betw een

– 47 and – 43?

c. W hat is th e probability th a t th e sam ple m ean is greater th an – 44? L056