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 38 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 6 comma 080 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 080 l b Over 38 EndFraction equals 160 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 174.2 lb and a standard deviation of 38.4.

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	174.2
std deviation   =σ=	38.4000
sample size       =n=	38
std error=σx̅=σ/√n=	6.2293

probability that the aircraft is​ overloaded :

probability =

P(X>160)

=

P(Z>-2.28)=

1-P(Z<-2.28)=

1-0.0113=

0.9887

as probability of it being overloaded is highly probable ; therefore one should lower the number of passenger it accommodated,