Question: Airline passengers get heavier In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) told airlines to assume that passengers average 190 pounds in the summer, including clothes and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 30 passengers.
(a) Explain why you cannot calculate the probability that a randomly selected passenger weighs more than 200 pounds.
(b) Find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds. Show your work. (Hint: To apply the central limit theorem, restate the problem in terms of the mean weight.)