Calculate z-score, percentile, and tail probability from value, mean, and standard deviation for normal distribution analysis.
Calculation
1) Formula: z = (x - μ) / σ
2) Substitute: z = (72.0000 - 65.0000) / 8.0000
3) Simplify: z = 7.0000 / 8.0000
4) Result: z = 0.8750
5) Percentile: Φ(z) × 100 = Φ(0.8750) × 100 = 80.92%
6) Right Tail: (1 - Φ(z)) × 100 = (1 - 0.809213) × 100 = 19.08%
Calculate z-scores and percentiles for normal distributions to quickly evaluate how far a value is from the mean.
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