Before every flight, the pilot must verify that the total weight of the load is

Question

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 3535 passengers, and a flight has fuel and baggage that allows for a total passenger load of 5 comma 8455,845 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 StartFraction 5 comma 845 l b Over 35 EndFraction equals 167 5,845 lb 35=167 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 174174 lb and a standard deviation of 38.338.3.

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean of the sampling distribution ( x ) = 174
standard Deviation ( sd )= 38.3/ Sqrt ( 35 ) =6.4739
sample size (n) = 35
GREATER THAN
P(X > 167) = (167-174)/38.3/ Sqrt ( 35 )
= -7/6.474= -1.0813
= P ( Z >-1.0813) From Standard Normal Table
= 0.8602

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