Question

The problem of matching aircraft to passenger demand on each flight leg is called the flight assignment problem in 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 144 passengers and a standard deviation of 42. Round probabilities in parts (a) through (c) to four decimal places. a) Suppose a Boeing 757 with a capacity of 186 passengers 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 94 passengers but no more than 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 Cheapfare Airlines wants to limit the probability that this flight is overbooked to 1%, how much capacity should the airplane that is used for this flight have? passengers e) What is the 65th percentile of this distribution?

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	144
std deviation   =σ=	42.0000

  probability that the demand will exceed the capacity of this airplane:

probability =

P(X>186)

=

P(Z>1)=

1-P(Z<1)=

1-0.8413=

0.1587

b)

  probability that the demand for this flight will be at least 94 passengers but no more than 200 passengers:

probability =

P(94<X<200)

=

P(-1.19<Z<1.33)=

0.9082-0.1170=

0.7912

c)

  probability that the demand for this flight will be less than 100 passengers:

probability =

P(X<100)

=

P(Z<-1.05)=

0.1469

d)

for 99th percentile critical value of z=		2.33
therefore corresponding value=mean+z*std deviation=			241.9~ 242

e)

for 65th percentile critical value of z=		0.39
therefore corresponding value=mean+z*std deviation=			160.4 ~160