Under older Federal Aviation Administration rules, airlines had to estimate the weight of a passenger as 185 pounds. (That amount is for an adult traveling in winter, and it includes 20 pounds of carry-on baggage.) Current rules require an estimate of 195 pounds. Based on data from the National Health and Nutrition Examination Survey, men have weights that are normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds.
a. If 1 adult male is randomly selected and is assumed to have 20 pounds of carry-on baggage, find the probability that his total is greater than 195 pounds. Round your answer to three decimal places.
b. If a Boeing 767-300 is full of 213 adult male passengers and each is assumed to have 20 pounds of carry-on baggage, find the probability that the mean passenger weight is greater than 195. Does the pilot have to be concerned about exceeding this weight limit?