The mean annual starting salary for marketing majors is $34,000 (Time, May 8, 2000). Assume that for the population of graduates with a marketing major, the population mean annual starting salary is $34,000, and the population standard deviation is $2,000. What is the probability that a simple random sample of marketing majors will have a sample mean within ± $250 of the population mean for each of the following sample sizes?
30, 100, 400