Question

Overbooking flights is a common practice of most airlines. A particular airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). Suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 278 tickets.

Question 2. What is the probability that the airline will not have enough seats for all the ticket holders who show for the flight?  (Use 3 decimal places.)

Answer 1

The binomial probability distribution of a random variable describing proportion can be approximated as a normal distribution if the sample size is large.

If sample size is n, the mean of the sampling distribution is p(the probability of success) and the standard error is .

Now the expected number of ticket holder that will fail to show for the flight is 0.04*278 = 11.12 11

The percentage of passengers not showing for the flight can be considered a normally distributed random variable with

Mean() = 0.04

Std. error() = = = 0.01175285

In order for the airline to not have enough seats for all the ticket holders who show for the flight, there should be less than (278−267) = 11 or 4.015% no show.

Hence,

P( x < 0.04015)

= P (z < (0.04015−0.04)/0.01175285) = P(z< 0.01276286) =0.505091 0.505 = 50.5 %