SOLUTION: 6.4 12/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 ​passen

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Question 1147830: 6.4 12/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 6 comma 923 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 6,923/43 equals 161
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 182.3 lb and a standard deviation of 38.8.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
What is the probability that the sample mean with n=43 is >161
z<(161-182.3)/38.8/sqrt(43)
z<-21.3*sqrt(43)/38.8
z<-3.60. this is for probability aircraft is NOT overloaded.
0.9998 is probability it is overloaded.