Q1) A public bus company official claims that mean waiting time for bus number 14 during peak hours is less than 10 minutes.  Karen took bus number 14 in peak hours on 18 different occasions.  Her mean waiting time was 7.2 minutes with standard deviation of 1.6 minutes.  At 0.01 significance level, test claim that the mean is less than 10 minutes. You may suppose that time spent waiting for bus 14 is normally distributed.

According to College Board's report, average tuition and fees at four year private colleges and universities in United States was $20,273 for academic year 2002 - 2003 and standard deviation was $4100. For random sample of 100 four year private U.S. colleges:

a) Compute the mean of the sampling distribution?

b) Compute the standard deviation of sampling distribution?

c) Compute the probability that mean tuition and fees of sample is greater than $20,000?

d) Determine probability that mean tuition and fees of sample is less than $18,000?

e) Compute the probability that mean tuition and fees of sample is within $410 of population mean?