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Math Help - Which distribution would this be?

  1. #1
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    Which distribution would this be?

    Someone receives 0,1 or 2 letters to his home per day with Probability 0.2, 0.7, and 0.1 respectively.

    If a year consists of 240 days in which he can receive letters, how many days are needed to get at least 99 letters with a probability of 0.99?

    Which distribution would this be? How should you approximate to solve the problem?
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  2. #2
    MHF Contributor matheagle's Avatar
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    You cna approximate this via the Central Limit Theorem or chebyshev's.
    This is a multinomial, you can calculate the mean and variance easily.
    The question seems to be, calculate n and I'd use the CLT.

    P(\sum_{i=1}^nX_i\ge 99)

    where X_i is the number of letters she receives on day i.
    and each X_i has that distribution you stated
    Next calculate the mean and variance and you can divide by n if you wish........

    P(\sum_{i=1}^nX_i\ge 99)=P(\bar X\ge {99\over n})
    and you may want a correction factor adjustment of 98.5 here

    \approx P\biggl(Z>{{98.5\over n}-\mu\over \sigma/\sqrt{n}}\biggr)

    You need to look up the normal percentile and then you solve for n, if I understood this correctly.
    Last edited by matheagle; December 23rd 2009 at 09:32 PM.
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  3. #3
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    Hey, thanks for your post! But when is continuity correction needed like in this case?
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  4. #4
    MHF Contributor matheagle's Avatar
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    Most people would ignore it, but you should understand that your rvs are integer based, 0,1 or 2. While the normal is continuous. Clearly there is a
    difference between greater than 99 and the statement greater than or equal to 99. The probablity of exactly 99 letters is being ignored, which it shouldn't be.
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