Question 1191807: Before every flight, a pilot must verify that the total weight of the load aboard their aircraft is less than the maximum allowable load for that type of aircraft. Suppose a commercial aircraft can carry 39 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,513 lb. Suppose the pilot sees that the plane is full and all passengers are adult men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,513 lb/39 passengers = 167 lb/passenger. Assuming that weights of adult men are normally distributed with a mean of 179.8 lb and a standard deviation of 37.6 lb, what is the probability that the aircraft is overloaded? (Round your answer to three decimal places; add trailing zeros as needed.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The sample distribution of weights of 39 passengers has a mean of 179.8 pounds and a sd of 37.6/sqrt(39)=6.020
so the probability the aircraft is NOT overloaded if 167 pounds or fewer is the average from a distribution of mean 179.8 and sd 6.020
z=(167-179.8)/6.020
z<-2.125
The probability of this occurrence is 0.0167. Therefore, the complement is the probability it is overloaded, and that is 0.9833, or 0.983
|
|
|
