Before every flight the pilot must verify that the total wei

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 41 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,765 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?6,765 lb/41=161lb 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 173lb and a standard deviation of 36.8.

The probability is approximately____

(Round to four decimal places as needed.)

Solution

mean=173*41 = 7093

standard deviation =36.8*41 = 1508.8

So the probability is approximately is

P(X>6765) = P((X-mean)/s >(6765-7093)/1508.8)

=P(Z>-0.22)

=0.5871 (from standard normal table)