Results 1 to 3 of 3

Math Help - Probability that a flight is over-booked

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    126

    Probability that a flight is over-booked

    An airline has 300 seats available on a flight to Australia. It is known from experience that on average only 99% of those who have booked seats actually arrive to the flight, the remaining 1% being called "no-shows". The airline therefore sells more than 300 seats. If more than 300 passengers then arrive, the flight is over-booked. Assume that the number of no-show passengers can be modelled by a binomial distribution.

    Question
    1) If the airline sells 303 seats:
    i)State a suitable distribution for the number of no show passengers and state a suitable approximation to this distribution, giving the values of any parameters.
    ii) Show that the probability that the flight is over-booked is 0.4165, correct to 4 decimal places.



    -----

    If anyone can help on this question please do because it's really annoying me as for part ii) especially, I keep the complimentary probability instead of the actual one and I have no idea where i'm going wrong! >_<


    please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,788
    Thanks
    1683
    Awards
    1
    If the airline sells 303 tickets and 301, 302, or 303 ticket holders actually show up for a flight then that flight will be over-sold. The probability that it happens is \sum\limits_{k = 301}^{303} {{{303} \choose k}\left( {.99} \right)^k \left( {0.01} \right)^{303 - k} }  = 0.41534.

    As you see, that answer is slightly off from the one given.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2006
    Posts
    126
    Ah thankyou - I understand now.

    The question used a poisson approximation for this but yours is more correct

    Thankyou! Plato!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Flight
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 2nd 2010, 07:43 PM
  2. Projectile Flight
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 23rd 2009, 12:00 PM
  3. angle of flight
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: September 8th 2008, 02:01 PM
  4. probability for over booked pasangers on a flight.
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 20th 2007, 09:19 PM
  5. Flight distance
    Posted in the Math Challenge Problems Forum
    Replies: 5
    Last Post: April 13th 2005, 10:45 PM

Search Tags


/mathhelpforum @mathhelpforum