(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 189.8 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 41.9 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 26 passengers. What is the approximate probability (±0.0001) that the total weight of the passengers exceeds 5324 pounds?

Explanation / Answer

:  P(xbar > 5324/26)

= P(xbar > 204.769)

= P(z > (204.769 - 189.8) / (41.9/sqrt(26)))

= P(z > 1.82)

= 1 - .9556

= .0034

There is a 0.52% chance that the total weight of the passengers exceeds 4,000 lbs.

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