Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the variable x as x = the number of people who actually show up for a sold-out flight on this plane. From past experience, the probability distribution of x is given in the table shown below. x 95 96 97 98 99 100 101 102 p(x) .05 .09 .13 .16 .24 .14 .06 .04 x 103 104 105 106 107 108 109 110 p(x) .04 .01 .02 .005 .005 .005 .0036 .0014 (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) =

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.