Bell Curve / z-Score and Percentile
z = (x - mu) / sigma; percentile from the standard normal CDF (Abramowitz + Stegun 26.2.17); curve letter band per the 68-95-99.7 rule. Teacher governs whether a normative curve is appropriate.
Formula and source
z = (raw - mean) / sd. percentile = standard-normal-CDF(z) * 100, via the Abramowitz + Stegun 26.2.17 approximation (~7.5e-8 absolute error). Curve bands: z >= 2 A+; 1 to 2 A; 0 to 1 B; -1 to 0 C; -2 to -1 D; below -2 F.
Abramowitz + Stegun, Handbook of Mathematical Functions, formula 26.2.17 (1965; National Bureau of Standards Applied Mathematics Series 55). Empirical 68-95-99.7 rule for the curve bands; pre-CCSS norm-referenced grading convention.
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