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Math Help - Empirical Rule & Chebyshev’s Theorem

  1. #1
    Amy
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    Question Empirical Rule & Chebyshev’s Theorem

    Calculate the probability of a result falling within 2.5 standard deviations from the mean, using

    a) Chebyshev’s Theorem

    b)
    Empirical Rule

    Please help
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  2. #2
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    I believe that you have not put enough information in the question like what is the mean all you told us was that its with in 2.5 of the mean.

    chebs thm

    P(M-OK< X < M+Ok)>= 1- 1/k^2
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Amy View Post
    Calculate the probability of a result falling within 2.5 standard deviations from the mean, using

    a) Chebyshev’s Theorem

    b)
    Empirical Rule

    Please help
    [/font]
    a) Chebyshev's inequality tells us that:

    P(|x-mu|>= k sigma) <= 1/k^2

    so P(|x-mu|) >= 2.5 sigma) <= 1/2.5^2 = 0.16

    So P(|x-mu| < 2.5 sigma) = 1-0.16 = 0.84.

    b) here I presume that we are to assume normality, so we look 2.5 up
    in a table of the standard normal distribution to get:

    So P(|x-mu| < 2.5 sigma) = 0.9876.

    RonL
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