Question: Weights of Water Taxi Passengers

A water taxi recently sank in Baltimore’s Inner Harbor. Among the 25 people on board, 5 died and 16 were injured.

An investigation revealed that the safe passenger load for the water taxi was 3500 pounds. Assuming a mean passenger weight of 140 pounds, the boat was allowed to carry 25 passengers, but the mean of 140 pounds was determined 44 years ago when people were not as heavy as they are today. (The sample mean weight of the 25 passengers aboard the boat that sank was found to be 168 pounds.)

The National Transportation and Safety Board suggested that the old estimated mean of 140 pounds be updated to 174 pounds, so the safe load of 3500 pounds would now allow only 20 passengers instead of 25.

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 the data from the National Health and Nutrition Examination Survey, assume that weights of men NOW are normally distributed with a mean of m = 172 pounds and a standard deviation of s = 29 pounds.

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

b. Find the probability that if an individual man is randomly selected, his weight will be greater than 175 pounds. SW

c. Find the probability that 20 randomly selected men will have a mean that is greater than 175 pounds (so that their total weight exceeds the safe capacity of 3500 pounds). SW

d. What weight separates the lightest 99.5% of men from the heaviest 0.5%? SW