Question: A random sample of size n = 70 is taken from a finite population of size N = 500 with mean μ = 220 and variance σ2 = 324.
a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard deviation of the sample mean.
b. What is the probability that the sample mean is less than 210?
c. What is the probability that the sample mean lies between 215 and 230?