Federal Aviation Administration rules require airlines to estimate the weight of a passenger as 195 pounds, including carry-on baggage. Men have weights (without baggage) that are normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds.
a. If one adult male is randomly selected and is assumed to have 20 pounds of carry-on baggage, how likely is it that his total weight is greater than 195 pounds?
b. If a Boeing 767-300 aircraft is full of 213 adult male passengers and each is assumed to have 20 pounds of carry-on baggage, how likely is it that the mean passenger weight (including carry-on baggage) is greater than 195 pounds? Does a pilot have to be concerned about exceeding this weight limit?