Weights of water taxi passengers it was noted in the chapter problem that when water taxi sank in Baltimore’s Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a “worst case” scenario in which all of the passengers are adult men.

(This could easily occur in a city that hosts conventions in which people of the same gender often travel in groups.) Based on data from the National Health and Nutrition Examination Survey, assume that weights of men are normally distributed with a mean of 172 lb. and a standard deviation of 29 lb.

a) If one, man is randomly selected, find the probability that he weighs less than 174 lb. (the new value suggested by the National Transportation and Safety Board).

b) With a load limit of 3500 lb., how many men passengers are allowed if we assume a mean weight of 140 lb.?

c) With a load limit of 3500 lb., How many men passengers are allowed if we use the new mean weight of 174 lb.?

d) Why is it necessary to periodically review and revise the numbers of passengers that are allowed to board?