# Because many passengers who make reservations do not show​ up, airlines often overbook flights

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Because many passengers who make reservations do not show​ up, airlines often overbook flights​ (sell more tickets than there are​ seats). A certain airplane holds 290 passengers. If the airline believes the rate of passenger​ no-shows is 5​% and sells 305 ​tickets, is it likely they will not have enough seats and someone will get​ bumped?

Use the normal model to approximate the binomial to determine the probability of at least 291  passengers showing up.

Should the airline change the number of tickets they sell for this​ flight? Explain.

Calculate the mean and the standard deviation using the formulas;- n *p and sqrt(n*p*q)

The probability of interest is that who show up,

p = 0.95

mean =  0.95 * 305  = 289.75

standard deviation =  =SQRT(0.95 * 0.05*305)

probability of at least 291 passengers showing up  = 1- =NORM.DIST(291,B2,B3,TRUE)  , apply the standard normal distribution  functions in excel to solve the problem.

The probability is very high​, so it is likely that they should  sell less .
​However, the decision also depends on the relative costs of not selling seats and bumping passengers.