Under older Federal Aviation Administration rules, airlines were required to est
ID: 3177556 • Letter: U
Question
Under older Federal Aviation Administration rules, airlines were required to estimate the weight of a passenger as 185 lb. (That amount is for an adult traveling in winter, and it includes 20 lb of carry-on baggage.) If the rules are now changed to use an estimate of 200 lb. Men now have weights that are normally distributed with a mean of 182.9 lb and a standard deviation of 40.9 lb. (based on Data Set I in Appendix B). a. If I adult male is randomly selected and assumed to have a 20 lb of carry-n baggage, find the probability that his total weight is greater than 200 lb. b. If a Boeing 767-300 aircraft is full of 213 adult male passengers and each is assumed to have 20 lb of carry-on baggage, find the probability that the mean passenger weight (including carry-on baggage) is greater than 200 lb. c. Based on the probability that you calculated in part b), does a pilot have to be concerned about exceeding this weight limit?Explanation / Answer
(a) = 182.9, = 40.9, x = 200
z = (x - )/ = (200 - 182.9)/40.9 = 0.4181
P(x > 200) = P(z > 0.4181) = 0.3379
(b) = 182.9, = 40.9, n = 213, x-bar = 200
z = (x - )/(/n) = (200 - 182.9)/(40.9/213) = 6.1019
P(x-bar > 200) = P(z > 6.1019) = 0
(c) No, the pilot need not be concerned since the probability that the mean weight is more than 200 lb is 0.
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