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If the mean is 100 and the standard deviation is 5, the lowest 5% of scores must be below what value? ?

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  • 1 month ago

    They must be below 100.

    Consider that this could be a few numbers at 95, and a equal number at 105.  The mean is 100, and the s.d. is 5. The lowest 5% is part of that pile of 95's.

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  • Look at z-scores

    http://www.z-table.com/

    At a z-score of -1.645, roughly, we have 5% of the scores below that point

    -1.645 = (S - 100) / 5

    -8.225 = S - 100

    100 - 8.225 = S

    91.775 = S

    5% of the scores will be below 92, roughly.  That makes sense.  68% will be between 95 and 105, 95% will be between 90 and 110, 99% will be between 85 and 115.  So, 2.5% will be less than 90, 16% will be less than 95 and 50% will be less than 100.

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