In 2006 at Ohio State University an overloaded passenger elevator fell between dorm floors and a student fatality occurred. Based on an assumption of a mean weight of 156.25 lbs per student, the elevator was rated to carry 16 passengers. After the incident, investigators claimed the elevator may have been 50% over its limit of 2500 lbs. Answer the following questions by hand and using the tables in the back of the book.

a) Given that the elevator was rated for 16 passengers with an assumed mean of 156.25 lbs, the elevator had a passenger limit of 2500 lbs. Assume that the elevator is loaded with 16 male passengers and assume the weights of men are normally distributed with a mean weight of 183.9 lbs and a standard deviation of 38.8 lbs. Find the probability that the 16 passengers have a mean weight greater than 156.25 lbs. Would your result indicate that the elevator is likely overloaded?

b) If 1 male passenger is randomly selected, what is the probability that they have a weight greater than 156.25 lbs? Compare this percentage with the one found in a). Which result is more relevant in evaluating the risk of the elevator being overloaded? Why?

c) Suppose the elevators rating was later changed to carry only 10 passengers and the load limit was changed to 2200 lbs. If all 10 passengers are male, find the probability that their mean weight is greater than 220 lbs. This would mean that their total weight is greater than the maximum capacity of 2200 lbs. Do the new ratings appear to be safe when the elevator is loaded with 10 male passengers?