In January 2003, US Airways Express Flight 5481, a small Beechcraft 1900D plane with 19 passengers, stalled seconds after take-off and crashed at the airport in Charlotte, N.C. The National Transportation Safety Board (NTSB) investigation found that one of the factors that contributed to this crash was the fact that the plane was overloaded and out of balance due to the use of incorrect passenger weight estimates, with the plane being apparently 580 lbs above its maximum allowable take-off weight, with a center of gravity below what was allowable. Apparently, though the pilots had computed the take-off weight of the plane, including the passengers, and found it to be within limits, they had done so using incorrect passenger weight estimates which had apparently not been revised since 1936 by the Federal Aviation Administration. The NTSB found that these incorrect weight estimates underestimated the average passenger weight by more than 20 lbs., resulting in the pilots having underestimated the total weight of the 19 passengers. Suppose you know that the weights of people in the U.S.A. are normally distributed with mean 200 lbs and standard deviation 40 lbs. A 30 seater plane has been certified to takeoff with a maximum passenger weight of 6360 lbs.

1) What is the probability that the total weight of a random collection of 30 passengers on board a full flight does not exceed this maximum allowable weight of 6360 lbs? (Hint: The total weight of the 30 passengers not exceeding 6360 is equivalent to saying that the sample mean weight of 30 passengers does not exceed 6360/30 = 212 lbs)) You must show your work in order to get credit for this problem

2) Based upon your answer in (1), do you think that the airline should operate the plane at full capacity? Justify your answer in a sentence or two