Please answer the following question with all work shown. Thank you! In response

Question

Please answer the following question with all work shown. Thank you!

In response to the increasing weight of airline passengers, the Federal Aviation Administration (FAA) 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 35 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 22 passengers. What is the approximate probability that the total weight of the passengers exceeds 4500 pounds? Use the four-step process to guide your work.

Explanation / Answer

for 22 passenger total mean weight =22*190=4180

and std deviation =35*(22)1/2 =164.1646

hence probabilty P(X>4500)=1-P(X<4500)=1-P(Z<(4500-4180)/164.1646)=1-P(Z<1.9493)=1-0.9744

=0.0256

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