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In 2003, the Federal Aviation Administration told airlines to assume the average weight of summer passengers (including clothing and carry-on bags) is 190 pounds, with a standard deviation of 35 pounds. Because the population includes male and female adults as well as children, the weights are not normally distributed, but they are nearly normal. A commuter plane carries 24 passengers. What is the probability that the total weight of the passengers exceeds 5000 pounds (the safe flying weight for the aircraft)?

Respuesta :

Answer:

Probability that the total weight of the passengers exceeds 5000 pounds is less than 0.0005%

Step-by-step explanation:

Given the average weight of summer passengers, [tex]\mu[/tex] = 190 pounds

and standard deviation, [tex]\sigma[/tex] = 35 pounds

Since the weights are nearly following normal so,

                      Z = [tex]\frac{X - \mu}{\sigma}[/tex] follows standard normal distribution

Let X represents total weight of the passengers.

So Probability(X>5000) = P( [tex]\frac{X - \mu}{\sigma}[/tex] > [tex]\frac{5000-190}{35}[/tex]) = P(Z > 137.43)

Since we will not be able to calculate this probability using Z table as the highest value in Z % table is given by 4.4172 which is way less than 137.43 so we can only say that this probability will be less than 0.0005% .

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