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 43 passangers, and a flight has fuel and baggage that allows for a total passanger load of 7,052 lb. The pilot sees the plan is full and all passangers are men. The aircraft will be overloaded ifthe mean weight fo the passangers is greater than 7,052/43=164 lb. What is the probabiltiy that the aircraft is overloaded? Should the pilot take action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 174.3 lb and a standard deviation of 36.1.

The probability is approximately __.

(Round to four decimal places as needed.)

Explanation / Answer

=174.3

=36.1

x=164

We have to find P(x>164) and we would use z score and normal distribution for it

z=(x-)/

=(164-174.3)/36.1

=-10.3/36.1

=-0.285

P(x>164 ) =P(z>-0.285) = 1-P(z<-0.285) =1-0.3878 =   0.6122

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