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 35 passengers, and a flight has
fuel and baggage that allows for a total passenger load of 5,705
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 5,705 lb35=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 180.6
lb and a standard deviation of 38.8. The probability is
approximately ______