The Economics Policy Institute periodically issues reports on wages of entry-level workers. The Institute reported that entry-level wages for male college graduates were $43.36 per hour, and for female college graduates were $37.60 per hour. Assume the standard deviation for male graduates is $2.50 and for female graduates is $2.10

a.What is the probability that a sample of 50 male graduates will provide a sample mean within $0.50 of the population mean, $43.36? (3 marks)

b.What is the probability that a sample of 50 female graduates will provide a sample mean within $0.50 of the population mean, $37.60? (3 marks)

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 $0.50 of the population mean? Why? (2 marks)

d.What is the probability that a sample of 120 female graduates will provide a sample mean more than $0.30 below the population mean? (2 marks)