In response to the increasing weight of airline passengers, the Federal Aviation

Question

In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190 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 42.7 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 25 passengers. What is the approximate probability (±0.0001) that the total weight of the passengers exceeds 5140 pounds

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Answer:

In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190 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 42.7 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 25 passengers. What is the approximate probability (±0.0001) that the total weight of the passengers exceeds 5140 pounds

The central limit theorem suggests that the sampling distribution of the mean will be close to a normal distribution for a sample of 25. So now we will proceed the final calculations using procedures that are applied to a normal distribution.

Average weight of 25 persons = 5140/25 =205.6

Standard error = 42.7/sqrt(25) =8.54

Z value for 205.6, z = (205.6-190)/8.54 =1.83

P( mean x >205.6) = P( z > 1.83)

=0.0336

There is a 3.36% chance that the total weight of the passengers exceeds 5140 lbs.

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