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

Respuesta :

Answer:

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

Step-by-step explanation:

[tex]\mu = 192[/tex]

[tex]\sigma = 31[/tex]

No. of passengers = n = 21

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

[tex]x = \frac{4432}{21} \sim 211[/tex]

[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{211-192}{31}[/tex]

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