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10 June, 18:40

A civil service exam yields scores with a mean of 81 and a standard deviation of 5.5. Using Chebyshev's Theorem what can we say about the percentage of scores that are above 92?

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  1. 10 June, 19:35
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    At most 12.5% of the scores are above 92.

    Step-by-step explanation:

    Chebyshev's theorem states that:

    At least 75% of the measures are within 2 standard deviations of the mean.

    At least 89% of the measures are within 3 standard deviations of the mean.

    In this problem, we have that:

    Mean = 81%

    Standard deviation = 5.5%

    Using Chebyshev's Theorem what can we say about the percentage of scores that are above 92?

    92 = 81 + 2*5.5

    So 92 is two standard deviations above the mean.

    By the Chebyshev's theorem, at least 75% of the measures are within 2 standard deviations of the mean. So at most 25% is more than 2 standard deviations from the mean. Chebyshev's theorem works with symmetric distributions, so, of those at most 25%, at most 12.5% are more than 2 standard deviations below the mean and at most 12.5% are more than 2 standard deviations above the mean.

    So at most 12.5% of the scores are above 92.
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