Question

In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 196 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 32 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 18 passengers. What is the approximate probability that the total weight of the passengers exceeds 3928 pounds

Answer 1

Answer: 0.0016

Explanation:

Given the following :

Population mean(m) = 196

Population Standard deviation (sd) = 32

Number of sample (n) = 18

Sample mean (x) = Total weight of sample / number of samples = 3928 / 18 = 218.2

Obtaining the test statistic (z) :

Z = [(x - m) / (sd/√n)]

Z = [(218.2 - 196) / (32/√18)]

Z = [(22.2 / 7.5424723)]

Z = 2.943

Hence,

P(Z > 2.94) = 1 - P(Z < 2.94)

= 1 - 0.9984

= 0.0016