# Loading Aircraft 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 Bombardier Dash 8 aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6200 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 6200 lb/37 = 167.6 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 189 lb and a standard deviation of 39 lb (based on Data Set 1 “Body Data” in Appendix B).

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Loading Aircraft 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 Bombardier Dash 8 aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6200 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 6200 lb/37 = 167.6 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 189 lb and a standard deviation of 39 lb (based on Data Set 1 “Body Data” in Appendix B).

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Step 1

Solution: We are given that:

Weights of men are normally distributed with a mean of 189 lb and a standard deviation of 39 lb

We are also given that the aircraft will be overloaded if the mean weight of the passengers is greater than 6200 lb/37 = 167.6 lb

Step 2

We have to find the probability that the aircraft is overloaded. Therefore, we have:

Step 3

Therefore, the probability that the aircraft ...

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