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 4040 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6 comma 7606,760 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 760 l b over 40 endfraction equals 169 6,760 lb 40=169 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 180.2180.2 lb and a standard deviation of 3838.
Accepted Solution
A:
Answer:Step-by-step explanation:X, the mean weight of passengers is N(180.2, 3838)No of passengers n = 4040std error = STd dev/ sqrt n= 60.38The probability that the aircraft is overloaded is 0.9920; since this is a greater than 50% chance, the pilot should either reduce the number of passengers on the plane or require them to reduce their baggage.The z-score for this is given byz = (X-μ)/σ = (169-180.2)/60.38 = -11.2/60.38 = -0.02Using a z-tableP(Z<-0.02) = 0.0080Prob for aircraft to be overloaded= P(Z>-0.02)=1-0.0080=0.9920