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Math Help - question on limit theorems hw!!!

  1. #1
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    question on limit theorems hw!!!

    Suppose that 2500 customers subscribe to a telephone exchange. There are 80 trunklines available. Any one customer has the probability of .03 of needing a trunkline on a given call. Consider the situation as 2500 trials with probability of success p=.03, what is the approximate probability that the 2500 customers will tie-up the 80 trunklines at any given time?
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  2. #2
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    Quote Originally Posted by lauren2988 View Post
    Suppose that 2500 customers subscribe to a telephone exchange. There are 80 trunklines available. Any one customer has the probability of .03 of needing a trunkline on a given call. Consider the situation as 2500 trials with probability of success p=.03, what is the approximate probability that the 2500 customers will tie-up the 80 trunklines at any given time?
    Let X be the random variable number of customers requiring a trunkline.

    X ~ Binomial(n = 2500, p = 0.03)

    Calculate \Pr(X \geq 80) = 1 - \Pr(X \leq 79).

    (In this golden age of technology the normal approximation to the binomial distribution is not required although its use would be valid).
    Last edited by mr fantastic; October 14th 2008 at 07:46 PM.
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  3. #3
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    So you are saying we can approx a binomil distribution using a normal distribution?
    so we would take mu to be np=2500*.03=75
    and sigma^2 to be np(1-p)=2500*.03*.97=72.75
    then find th z-score and use a table for the answer??
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  4. #4
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    You can use binomial distribution, when the problem satifies the 4 characteristics listed below :

    . The experiment consists of n identical trials
    . Each trial results in 1 of 2 outcomes called 'success' and 'failure'
    . P('success') = p remains constant from trial to trial, and p('failure') = 1-p
    . Each trials is independent, i.e. not affected by results of other trials.

    This characteristics perfectly suits the problem that you brought up therefore i think it is best to use binominial distribution to solve the problem. If i am not wrong u need to find th z-score and use a table for get the answer. Remember to apply the continuity correction for these kind of problem. Hope it helps.
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