According to the College Board's report, the average tuition and fees at four year private colleges and universities in the United States was $20,273 for the academic year 2002 - 2003 and the standard deviation was $4100. For a random sample of 100 four year private U.S. colleges:
a. What is the mean of the sampling distribution?
b. What is the standard deviation of the sampling distribution?
c. What is the probability that the mean tuition and fees of the sample is greater than $20,000?
d. What is the probability that the mean tuition and fees of the sample is less than $18,000?
e. What is the probability that the mean tuition and fees of the sample is within $410 of the population mean?