When a 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.) Assume that weights of men are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb (based on Data Set 1 in Appendix B).
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 male passengers are allowed if we assume a mean weight of 140 lb?
c. With a load limit of 3500 lb, how many male passengers are allowed if we use a new mean weight of 182.9 lb?
d. Why is it necessary to periodically review and revise the number of passengers that are allowed to board?