Airlines sometimes overbook fights. Suppose that for a plane with 100 seats, an

Question

Airlines sometimes overbook fights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the variable x as the number of people who actually show up for a sold-out flight. From past experience, the probability distribution of x is given in the table shown below: (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) you are trying to get a seat on 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) You may need to use the appropriate table in Appendix A to answer this question.

Explanation / Answer

(a)

The flight will accomodate all the persons if number of persons who show up is less than eqaul to 100. So requried probability is

P(X <=100) = P(X=95) + P(X=96) + ...+P(X=100) = 0.04 +0.10 + 0.11+ 0.16 + 0.24+0.17 = 0.82

(b)

By the complement rule, the probability that not all the persons accomodated is

P(not all the persons accomodated) = 1 - 0.82 = 0.18

(c)

You will be able to get the seat if X is less than equal to 99. So

P(X < =99) =  P(X=95) + P(X=96) + ...+P(X=99) = 0.04 +0.10 + 0.11+ 0.16 + 0.24= 0.65

(d)

You will be able to get the seat if X is less than equal to 97. So

P(X < =97) =  P(X=95) + P(X=96) + P(X=97)= 0.04 +0.10 + 0.11= 0.25

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