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 43 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 7 comma 009 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 009 l b Over 43 EndFraction equals 163 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 175.6 lb and a standard deviation of 37.8.

Answer 1

for standard error of mean =standard deviation/sqrt(n)=37.8/sqrt(43)=5.7644

hence P( aircraft is​ overloaded )=P(X>163)=P(Z>(163-175.6)/5.7644)=P(Z>-2.19)=0.9857

as probability of this happening is very large ; therefore to avoid overloading pilot should empty beggage for safety measure.