The problem of matching aircraft to passenger demand on each flight leg is called theflight assignment problemin the airline industry.Suppose the demand for the 6 p.m. flight from Toledo Express Airport to Chicago's O'Hare Airport on Cheapfare Airlines is normally distributed with a mean of 139 passengers and a standard deviation of 44.

Round probabilities in parts (a) through (c) to four decimal places.

a) Suppose a Boeing 757 with a capacity of 187passengers is assigned to this flight.What is the probability that the demand will exceed the capacity of this airplane?

b)What is the probability that the demand for this flight will be at least 89 passengers but no morethan 200 passengers?

c) What is the probability that the demand for this flight will be less than 100 passengers?

Round answers in parts (d) and (e) to the nearest whole number.

d) If CheapfareAirlines wants to limit the probabilitythat this flight is overbooked to 2%, how much capacity should the airplane that is used for this flight have?passengers

e) What is the 29th percentile of this distribution?