According to College Board's report, the average tuition and fees at 4 year private colleges and universities in United States was $20,273 for the academic year 2002 - 2003 and standard deviation was $4100. For the random sample of 100 four year private U.S. colleges:
a. Find out the mean of the sampling distribution?
b. Find out the standard deviation of sampling distribution?
c. Find out the probability that the mean tuition and fees of sample is greater than $20,000?
d. Find out the probability that the mean tuition and fees of sample is less than $18,000?
e. Find out the probability that the mean tuition and fees of sample is in $410 of population mean?