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I'm not sure which method is correct (statistics)

  1. Jun 21, 2010 #1
    1. The problem statement, all variables and given/known data


    3. The attempt at a solution

    The textbook says the answer is 0. I think they get that by saying that 5% of 240 is 12. So the plane is overbooked by 12. So there are 252 people booked on the plane. Then the binomial expectation is (252*0.95)=239.4. Which means they payout nothing since less than 240 people are expected to show up.

    However, I don't really think that's logical...the way I would do it is:

    expectation=(200)(probability that 1 is bumped off)+(400)(probability that 2 are bumped off)+...etc, up to 12. Because how could they only be expected to pay out 0 as the textbook says, when sometimes they WILL have to pay out something (there is always a chance someone will get bumped off), which makes it >0.

    Just to add, for example, if they were paying a trillion dollars for every person bumped off, the expected value wouldn't be 0 intuitively...just because they have a low chance of paying that, doesn't mean it can't happen.

    This is all the solutions manual says:
     
    Last edited: Jun 21, 2010
  2. jcsd
  3. Jun 21, 2010 #2

    Mark44

    Staff: Mentor

    This sounds eminently reasonable to me.
    But you aren't given any information about these probabilities. All you are given is that, on average, 5% of the booked passengers don't show up.
     
  4. Jun 21, 2010 #3
    But that's enough to find the probabilities using a binomial distribution, isn't it?

    Ex, to find the probability that one passenger is overbooked:

    =252C241(.95)^241(.05)^11
     
  5. Jun 21, 2010 #4

    Mark44

    Staff: Mentor

    I guess this will work, but it seems the long way around.
     
  6. Jun 21, 2010 #5
    Yea it will take a lot longer, but the answer won't be 0 for sure though. Like I said, how could the expected payout be zero when there IS a chance they will pay SOMETHING out. That's what I've done for every other question, for http://en.wikipedia.org/wiki/Expected_value#Examples"
     
    Last edited by a moderator: Apr 25, 2017
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