# Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations.

## Question:

From past experience, the probability distribution of x is given in the following table:

x p(x)

95 ………………. 0.05

96 ………………. 0.10

97 ………………. 0.12

98 ………………. 0.14

99 ………………. 0.24

100………………. 0.17

101………………. 0.06

102………………. 0.04

103………………. 0.03

104………………. 0.02

105 ………………. 0.01

106 ………………. 0.005

107 ………………. 0.005

108 ………………. 0.005

109 ………………. 0.0037

110 ………………. 0.0013

a. What is the probability that the airline can accommodate everyone who shows up for the flight?

b. What is the probability that 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? What if you are number 3?

Distribution

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