(15.36) In response to the increasing weight of airline passengers, the Federal

Question

(15.36) In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190.1 pounds in the summer, including clothing and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 40.1 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 23 passengers. What is the approximate probability (±0.0001) that the total weight of the passengers exceeds 4763 pounds?

Explanation / Answer

mean = 190.1
std. dev. = 40.1
n = 23

For the flight of 23 passangers,
mean = 23*190.1 = 4372.3
std. dev. = 40.1*sqrt(23) = 192.3128

P(X > 4763)
= P(z > (4763 - 4372.3)/192.3128)
= P(z > 2.0316)
= 0.0211

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