Question

Airline Overbooked: Airlines don't like flights with empty seats. Suppose that, on average, 95 percent of all ticket-holders show up for a flight. if the airline sells 105 tickets for a 100-seat flight, what is the probability that the flight will be overbooked?

. Determine how the probability of overbooking varies as the number of tickets sold varies from 100 through 115, Hint Use a one-way data table

. Show how the probability of overbooking varies as the number of tickets sold varies from 100 through 115, and the probability that a ticket holder shows up varies from 80 percent through 95 percent. Hint: Use a two-way data table

Answer 1

P(overbooked)= P( X>100) = P(X=101)+P(x=102)+P(x=103)+P(104)+P(x=105)

n = 105 p=0.95 q=1-p=0.05

So using binomial distribution we can find above probability by using excel command as follows,

= 1-BINOM.DIST(100,105,0.95,1) =0.3924

P(overbooked)=0.3924

now if the number of ticket sold = 115 that is n=115

So the command is as follows,

P(overbooked) = 1-BINOM.DIST(100,115,0.95,1) =0.9993

And if n=115 and p=0.80 then the command is as follows

P(overbooked) = 1-BINOM.DIST(100,115,0.80,1) = 0.01936

This much probability varies when n and p changes.