The problem of matching aircraft to passenger demand on each flight leg is called the flight assigvlment in the airline industry. Spill is defined as the number of passengers not carried because the aircraft's capacity is insufficient. A solution to the flight assignment problem at Delta Airlines was published in Interfaces (Jan.-Feb.

1994). The authors-four Delta Airlines researchers and a Georgia Tech professor (Roy Marsten)-demonstrated their approach with an example in which passenger demand for a particular flight leg is normally distributed with a mean of 125 passengers and a standard deviation of 45. Consider a Boeing 727 with a capacity of 148 passengers and a Boeing 757 with a capacity of 182. ,,

a. What is the probability that passenger demand will exceed the capacity of the Boeing 727? The Boeing 757?

b. If the 727 is assigned to the flight leg. what is the probability that the flight will depart with one or more empty seats? Answer the same question for the Boeing 757.

c. If the 727 is assigned to the flight, what is the probability that the spill will be more than 100 passengers?