Before everyflight, 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 37

37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6 comma 105

6,105 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 6 comma 105 l b Over 37 EndFraction equals 165

6,105lb37=165 lb. What is the probability that the aircraft isoverloaded? Should the pilot take any action to correct for an overloadedaircraft? Assume that weights of men are normally distributed with a mean of 176.2

176.2 lb and a standard deviation of 36.8

36.8.

The probability is approximately

nothing

.