When a water taxi sank in the Baltimore Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lbs. It was also noted that the mean weight of a passenger was assumed to be 140 lbs. Assume a "worst case" scenario in which all 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 the weight of men are normally distributed with a mean of 172 lbs and a standard deviation of 29 lbs. Can you help me with the following questions?
a) If one man is randomly selected, what is the probability that he weighs less than 174 lbs (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 lbs?
c) With a load limit of 3500 lb, how many men passengers are allowed if we use the new mean weight of 174 lbs?
d) Why is it necessary to periodically review and revise the number of passengers that are allowed to board?
a) Solution: Let X be the weight of a randomly selected man. Then X follows a normal distribution with mean of 172 lbs and a standard deviation of 29 lbs. Set Z=(X-172)/29. So, Z follows N(0, 1), the standard normal distribution. Hence, the probability that he weighs less than 174 lbs is
The weights of water taxi passengers are determined.