Before covid, the Federal Aviation Administration changed passenger weight standards to an average of 190 pounds per passenger in the summer and 195 in the winter. This includes the passenger, clothing, and carry-on luggage. It is believed that the population standard deviation is about 35 pounds. Weights are not normally distributed, especially as the population includes men, women, and children, but they are not very non-normal.

(a) A wide-body jet (two aisles) holds 125 passengers. What is the probability that, in the summer, the average weight of the passengers is less than 188 pounds? Include a graph with your answer.

(b) A communter plane carries 30 passengers. What is the probability that, in the summer, the total weight of the passengers exceeds 6150 pounds? Include a graph with your answer. (Hint - the total weight is n* the average weight per passenger. Use this to find the distribution.)