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In 2005, the Federal Aviation Administration (FAA) updated its passenger weight standards to an average of 190 pounds in the summer (195 in the winter). This includes clothing and carry-on baggage. The FAA, however, 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 25 passengers. What is the approximate probability that, in the summer, the total weight of the passengers exceeds 5200 pounds

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Answer: 0.0051

Step-by-step explanation:

Given the following :

Average Population weight (m) = 190

Population standard deviation (σ) = 35

Total weight of 25commuters (x) = 5200

Sample mean = 5200 /25 = 108

Sample standard deviation = standard error :

σ / √n = 35/√25 =

35/5 = 7

Zscore = (x - m) / standard error

Zscore = (208 - 190) / 7

Zscore = 18 / 7

= 2.57

P( Z > 2.57) = 1 - p(Z < 2.57)

P(z < 2.57) = 0.9949

1 - p(Z < 2.57) = 1 - 0.9949 = 0.0051

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