STAT 1000 Question 6(5 points)

Service times for customers at a post office follow some right-skewed distribution with mean2.97minutes and standard deviation1.82minutes. (a) Can you calculate the probability that the average service time for the next two customersis less than2.7minutes? If you can,then calculate it. If you can't, explain why not.

(b) What is the probability that the mean servicetime for a random sample of31customers is between 2.5and 3.19minutes? (c) What is the probability that the total service time for the next 48customers exceeds 161.73minutes? (Assume that the next 48customers represent a simple random sample and that there is always a customer waiting in line.) (d) What is the probability that the mean service time for a random sample of 58customers is exactly 3.65minutes?

(e) Are the probabilities you calculated in (b) and (c) exact or approximate? Explain.