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 224 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 224 l b Over 43 EndFraction equals 168 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 178.2 lb and a standard deviation of 37.

Answer 1

From the given information,

Mean=178.2

Sd=37

Now,

By using standard normal probability calculator,

P(X>168)=0.6086

Hence,

Yes,  Pilot has to take an action to correct for an overloaded​ aircraft.

Thank you.