Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the variablexas the number of people who actually show up for a sold-out flight. From past experience, the probability distribution ofxis given in the table shown below:
|
x
|
95
|
96
|
97
|
98
|
99
|
100
|
101
|
102
|
|
p(x)
|
.04
|
.09
|
.13
|
.16
|
.22
|
.16
|
.07
|
.04
|
|
x
|
103
|
104
|
105
|
106
|
107
|
108
|
109
|
110
|
|
p(x)
|
.04
|
.01
|
.02
|
.005
|
.005
|
.005
|
.0037
|
.0013
|
(a) What is the probability that the airline can accommodate everyone who shows up for the flight?
P(airline can accommodate everyone who shows up) =
(b) What is the probability that not all passengers can be accommodated?
P(not all passengers can be accommodated) =
(c) If you are trying to get a seat on such a flight and you are number 1 on the standby list, what is the probability that you will be able to take the flight?
P(number 1 standby will be able to take the flight) =
What if you are number 3?
P(number 3 standby will be able to take the flight) =