Each
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-score is calculated using the formula
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where
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is the student's score,
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is the class average, and
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is the class standard deviation.
So, if you substitute Carol's results, you get that
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.
Doing the same for Zachary and Matilda, you will have three equations with only two unknowns. So, you can find what value of
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and
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work for two of them, and then figure out for the third whether the problem is an incorrect
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or
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and then find the correction that is needed.