A random sam ple of size n = 70 is taken from a finite population of size N = 500 with m ean μ = 220 and variance σ 2 = 324.

a. Is it necessary to apply th e finite population correction factor? Explain. Calculate th e 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 less than 210?

c. W hat is th e probability th a t th e sam ple m ean lies betw een 215 and 230? L056