How to calculate a curved score with the following stats:
Min: 13.0
Max: 61.5
Mean: 44.48
Standard Deviation: 10.86
If a students grade was 80%, what would his new grade be?
Without loss of generality, we can assume that the distribution of scores are normal.
Let X be the random variable denoting the distribution of scores. Hence, X ~ N(44.48, 10.86)
Thus, (X - 44.48)/10.86 ~ N(0,1) approximately.
Let, P(X < a) = 0.8 i.e. P[(X -
44.48)/10.86 < (a - 44.48)/10.86] = 0.8 i.e.
[(a - 44.48)/10.86] = 0.8 i.e.
[(a - 44.48)/10.86] =
(0.8) i.e. (a - 44.48)/10.86 = 0.842 i.e. a = 53.6241.
Hence, his new score is 53.6241.
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