For any given flight, an airline tries to sell as many tickets as possible. Suppose that on average, 10% of ticket holders fail to show up, all independent of one another. Knowing this, an airline will sell more tickets than there are seats available (i.e., overbook the flight) and hope that there is a sufficient number of ticket holders who do not show up to compensate for its overbooking. Using the Central Limit Theorem, determine n, the maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane. Use the de Moivre-Laplace 1/2-correction in your calculations. Hint: You may have to solve numerically a quadratic equation.

Question

beta · Accepted Answer

475

Q · Answer

Let N be the numbers of passengers that show up. So p=0.9 and E[N]=0.9n and σ=(n*0.1*0.9)^1/2=0.3*n^1/2.
Using Moivre-Laplace we have P(N≥300.5)≈0.01
Next you should use CLT, solving quadratic equation and find value of n

Ken · Answer

What is the answer?

r · Answer

The answer by beta is correct for a question with different parameters not for the above question.