Question

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, hat is the probability that the aircraft is​ overloaded? Round your answer to three decimal places; add trailing zeros as needed. P(aircraft is​ overloaded) = [OLProb].

Answer 1

Solution :

Given that,

mean = = 179.8 lb

standard deviation = = 37.6 lb

n = 39

=   = 179.8 lb

= / n = 37.6/ 39 = 6.02

P( > 167) = 1 - P( < 167)

= 1 - P[( - ) / < (167 - 179.8) /6.02 ]

= 1 - P(z <-2.13)

Using z table,    

= 1 - 0.017

= 0.983

Yes. Because the probability is​ high, the pilot should take action by somehow reducing the weight of the aircraft.