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Homework Help: Probability question in telephone network failures

  1. Jan 16, 2007 #1
    Hi,

    I have this problem

    1. The problem statement, all variables and given/known data

    In telephone network, an average number of failures during a month for one telephone owner is 8. What is the probability that some telephone owner will experience more than 4 failures?

    3. The attempt at a solution

    I have no idea what distribution should I use to model this problem. So far I've come up with binomial distribution with probability of individual event 8/k, where k is number of connection the telephonist will make during a month.

    But that seems really odd to me...

    Could someone help please?

    Thank you.
     
  2. jcsd
  3. Jan 16, 2007 #2

    AlephZero

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    Science Advisor
    Homework Helper

    So you have the situation where there are k trials (attempted calls), the probability of "success" (i.e. there is a fault) is 8/k, and k is probably large.

    What distribution is an approximation to the Binomial(n,p) as n becomes large and np stays constant?
     
  4. Jan 16, 2007 #3
    One way is to approximate it with Poisson distribution, but can I solve it using Central Limit Theorem? Which one is better?
     
  5. Jan 16, 2007 #4
    I tried to finish it using the Poisson distribution and it seems ok.

    Anyway, using Central Limit Theorem I got result depending on n, is it ok?
     
  6. Jan 16, 2007 #5
    Yeap, I think Poisson distribution is more appropriate here.
     
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