The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were $18.80 per hour in 2011 (Economic Policy Institute website, March 30, 2012). Assume the standard deviation for male graduates is $2.30, and for female graduates it is $2.05.

a. What is the probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68?

b. What is the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80?

c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $.50 of the population mean? Why?

d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean?