# 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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- MorningfoxLv 71 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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- 1 month ago
Look at z-scores

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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- MorningfoxLv 71 month agoReport
But even a simple uniform distribution would have a different answer.

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