before every flight, the pilot must verify that the total weight of the load for

Question

before every flight, the pilot must verify that the total weight of the load for the aircraft. the aircraft can carry 36 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,048 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 he 6,048lb/36=168 lb. what is the probability that the aircraft is overloaded? should the pilot take any action to correct for an overload aircraft? Assume that weights of men are normally distributed with a mean of 176.5 lb and a standard deviation of 38.5.

Explanation / Answer

Ans:

standard error of sample mean=38.5/sqrt(36)=6.42

z score for sample average of 168:

z=(168-176.5)/6.42=-1.32

P(z>-1.32)=0.9066

90.66% of the time aircraft will be overloaded.So,piot should take action to correct fo an overloaded aircraft.

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