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 40 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 6 comma 520 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 6 comma 520 l b Over 40 EndFraction equals 163 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 181 lb and a standard deviation of 37.2. The probability is approximately nothing.

Answer 1

Let x be the maximum allowable weights of men for the aircraft.

x follows normal distribution with mean ( µ ) = 181 and standard deviation (σ) = 37.2

be the average weigh of 40 passengers = 6520 /40 = 163

According to sampling distribution of sample mean , follows approximately normal distribution with mean ( µ ) = µ = 181 and standard deviation( σ) = = = 5.8818

We are asked to find P( > 163 )

=

= P( z > -3.06 )

= 1 - P( z < -3.06 )

= 1 - 0.0011

= 0.9989

The probability is approximately 0.9989