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80% is between -1.2815 and 1.2815 in standard units 90% is between -1.96 and 1.96 15/r.m.s. error = 1.2815 score/r.m.s. error = 1.96 => score = 15*1.96/1.2815 Now, when rounding 1.2815 to either 1.281 or 1.282 you'll get slightly different result
Here is an idea, not the answer: S[i] = 5*Xr[i] - 1*Xw[i], where S[i] is Score, Xr[i] - right answer and Xw[i] - wrong answer for the i-th student The key here is to remember that there are exactly 10 questions each student answers, so Xw[i] = 10 - Xr[i]

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