(Solved): Before every flight, the pilot must verify that the total weight of the load is less than the maxim ...

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 \( 7,267 \mathrm{lb} \). 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 \( \frac{7,267 \mathrm{lb}}{43}=169 \mathrm{lb} \). What is the probability that the alreraft 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 \( 175.8 \mathrm{lb} \) and a standard deviation of \( 35.3 \). The probability is approximately (Round to four decimal places as needed.)