Question

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

Answer 1

Answer: 0.0051

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