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Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry ​passengers, and a flight has fuel and baggage that allows for a total passenger load of lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than lb. What is the probability that the aircraft is​ overloaded? should the pilot take any action to correct for an overloaded​ aircraft? assume that weights of men are normally distributed with a mean of lb and a standard deviation of.

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abiolataiwo2015

The  probability that the aircraft is​ overloaded is 99.92%.

Probability

Given:

Population mean (μ)=177.9 lb

Population standard deviation (σ)=35.9 lb

Sample size (n)=40

a. Probabilty

First step is to calculate the Standard error

Standard error=σ/√n

Standard error=35.9/√40

Standard error=35.9/6.32

Standard error=5.68

Second step is to calculate the probability

P(x>160)=P(z>160-177.9)/5.68)

P(x>160)=P(z>17.9/5.68)

=P(z>-3.15)

=0.9992×100

=99.92%

b. Yes, the pilot should take an action to correct for an overloaded​ aircraft because the  mean weight is higher than 160 lb.

Therefore the probability that the aircraft is​ overloaded is 99.92%.

Learn more about probability here:https://brainly.com/question/24756209

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The complete question is:

Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 40 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,400 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,400 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6400 lb over 40 = 160 lb.

a. What is the probability that the aircraft is overloaded?

b. Should the pilot take any action to correct for an overloaded aircraft? Assume that the weights of men are normally distributed with a mean of 177.9 lb and a standard deviation of 35.9.

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