Before every flight, the pilot must verify that the total weight of the load is

Question

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

42

passengers, and a flight has fuel and baggage that allows for a total passenger load of

7,056

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

StartFraction 7 comma 056 l b Over 42 EndFraction equals 1687,056 lb42=168

lb. What is the probability that the aircraft isoverloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of

183.7

lb and a standard deviation of

36.3

Explanation / Answer

here std error of mean =std deviaiton/(n)1/2 =36.3/(42)1/2 =5.6012

therefore probability that the aircraft is overloaded=P(X>168)=1-P(X<168)=1-P(Z<(168-183.7)/5.6012)

=1-P(Z<-2.8030)=1-0.0025 =0.9975

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