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Math Help - Central Limit Theorem

  1. #1
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    Central Limit Theorem

    What is the probability that after 80 rolls of a die, the total sum of the upturned faces will exceed 260?

    So far I have (1 - P(X1+...+X80 - 80(mean X1) <= 260)) / (std. dev.)(sqrt(80)).

    Am I doing this correctly, and if so, how do I find the mean and std. deviation to put into the equation?
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  2. #2
    MHF Contributor matheagle's Avatar
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    upturned faces=sum of the spots?

    Then you want

    P(\sum_{i=1}^{80}X_i>260)
    I would put in a correct factor and approximate it with a normal...

    \approx P(\sum_{i=1}^{80}X_i>260.5)

    where the X's are iid from the distribution that puts 1/6 probability on {1,2,3,4,5,6}.
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