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

Question:

Define the variable x as the number of people who actually show up for a sold-out flight. From past experience, the population distribution of x is given in the following table:

x Proportion x Proportion 95 .05 103 .0300 96 .10 104 .0200 97 .12 105 .0100 98 .14 106 .0050 99 .24 107 .0050 100 .17 108 .0050 101 .06 109 .0037 102 .04 110 .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?

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