Normal distribution probability and percentile

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. Men have weights that are normally distributed with a meanof 172 pounds and a standard deviationof 29 pounds.

a. If 1 adult male is randomly selected and is assumed to have 20 pounds of carry-on baggage, find the probabilitythat his total 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, find the probability that the mean passenger weight (including carry-on baggage) is greater than 195 pounds. Does a pilot have to be concerned about exceeding the weight limit?

In this solution, a known normal distribution is used to find the probability of an event and the percentile of an event.