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inysia [295]
3 years ago
8

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
Mathematics
1 answer:
Rufina [12.5K]3 years ago
7 0

Answer:

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

Step-by-step 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 = \frac{4432}{21} \sim 211

Z=\frac{x-\mu}{\sigma}\\Z=\frac{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

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