Question 1146567
"Scores below the top 78% and above the bottom 6%" is another way of saying scores between 6% and 22%.
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The rest of the info given isn't needed.
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First, we will find what the numerical score is for 22%.
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Go to a z-table and find where the value is 0.22. (Or, the closest value that's below 0.22, since the question states these are scores BELOW 22%...or, as they put it, scores below the top 78%.)  The z-score where this occurs is -0.78. (**NOTE: The fact that the z-score is -0.78 and the question states 78% is purely coincidental.)
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Plug this into the following formula:
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(x - mean)/SD = -0.78
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(x - 75.1)/9.1 = -0.78
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Solve for x:
(x - 75.1)/9.1 = -0.78
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(-0.78)(9.1) = (x - 75.1)
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-7.098 = x - 75.1
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x = 68.002
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So, the 22% score is 68 (rounded off).
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Next, we will find what the numerical score is for 6%.
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Go to a z-table and find where the value is 0.06. (Or, the closest value that's above 0.06, since the question states these are scores ABOVE 6%.)  The z-score where this occurs is -1.55.
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Plug this into the following formula:
<pr>
(x - mean)/SD = -1.55
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(x - 75.1)/9.1 = -1.55
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Solve for x:
(x - 75.1)/9.1 = -1.55
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(-1.55)(9.1) = (x - 75.1)
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-14.105 = x - 75.1
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x = 60.995
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So, the 6% score is 61 (rounded off).
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The numerical limits for a D grade are "higher than 61 and less than 68."