Question

In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 192 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 31 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 21 passengers. What is the approximate probability that the total weight of the passengers exceeds 4432 pounds

Answer 1

The approximate probability that the total weight of the passengers exceeds 4432 pounds is 0.2709

Explanation:

`\mu = 192`

`\sigma = 31`

No. of passengers = n = 21

We are supposed to find the approximate probability that the total weight of the passengers exceeds 4432 pounds

`x = (4432)/(21) \sim 211`

`Z=(x-\mu)/(\sigma)\\Z=(211-192)/(31)`

Z=0.612

refer z table

P(Z<211)=0.7291

P(Z>211)=P(Z>4432)=1-0.7291=0.2709

Hence the approximate probability that the total weight of the passengers exceeds 4432 pounds is 0.2709