Results 1 to 2 of 2

Math Help - Binomial Distribution Problem on airline overbooking

  1. #1
    Newbie
    Joined
    Jan 2012
    Posts
    1

    Binomial Distribution Problem on airline overbooking

    1) How many tickets should an airline company sell for a 120 seat plane if they have averaged 15 percent of the people not showing up?
    2) What if in a simplified world all tickets are 250dollars and a person with a ticket who cannot fly due to overbooking receives 400dollars. Does this change the answer to number 1?
    3) Now on this same 120 seat plane, If Airline1 partners with Airline2 with 100 seats on the flight alloted for A1 and 20 seats alloted for A2
    and the two companies sell tickets independently and still the same 15
    percent do not show up, how many tickets should each company sell?

    For question one, at first I believe to find n, which is the number of tickets i should sell would be n x .85 = 120. So i believe n = 142. Is this correct for question number one?

    I am very confused for the second question. I am not sure how to find if the airline still makes a profit from selling 142 tickets.

    if x = number of people who DON'T show up then
    P (x<22) = binomcdf(142, .15, 21) = .6206
    So the probability that fewer than 22 people (15) don't show up then we would have overbooking and have to pay back 400 dollars... Except I dont know how to figure out how many would be overbooked. I'm not sure if i'm heading in the right direction... Can somebody please help me out?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Binomial Distribution Problem on airline overbooking

    Quote Originally Posted by yoyostatplease View Post
    1) How many tickets should an airline company sell for a 120 seat plane if they have averaged 15 percent of the people not showing up?
    2) What if in a simplified world all tickets are 250dollars and a person with a ticket who cannot fly due to overbooking receives 400dollars. Does this change the answer to number 1?
    3) Now on this same 120 seat plane, If Airline1 partners with Airline2 with 100 seats on the flight alloted for A1 and 20 seats alloted for A2
    and the two companies sell tickets independently and still the same 15
    percent do not show up, how many tickets should each company sell?

    For question one, at first I believe to find n, which is the number of tickets i should sell would be n x .85 = 120. So i believe n = 142. Is this correct for question number one?

    I am very confused for the second question. I am not sure how to find if the airline still makes a profit from selling 142 tickets.

    if x = number of people who DON'T show up then
    P (x<22) = binomcdf(142, .15, 21) = .6206
    So the probability that fewer than 22 people (15) don't show up then we would have overbooking and have to pay back 400 dollars... Except I dont know how to figure out how many would be overbooked. I'm not sure if i'm heading in the right direction... Can somebody please help me out?
    There is no answer to part 1 as there is no cost model associated with the question. Without further qualification they should not sell more than 120 tickets.

    The other two parts you solve by maximising the expected revenue.

    CB
    Last edited by CaptainBlack; January 12th 2012 at 10:44 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial distribution problem (I think)
    Posted in the Statistics Forum
    Replies: 3
    Last Post: February 3rd 2011, 12:04 PM
  2. Binomial Distribution Problem
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: July 10th 2010, 08:47 PM
  3. Airline overbooking problem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 2nd 2009, 05:44 PM
  4. Airline Report Problem
    Posted in the Statistics Forum
    Replies: 8
    Last Post: April 19th 2009, 09:50 PM
  5. [SOLVED] [SOLVED] Airline Passenger Seats/Overbooking Probability
    Posted in the Statistics Forum
    Replies: 5
    Last Post: April 17th 2008, 02:36 PM

Search Tags


/mathhelpforum @mathhelpforum