๐Ÿ“Š Probability & Statistics

Z-Score & Normal Distribution Calculator

Convert raw scores into standard Z-scores, calculate p-values, percentiles, and visualize shaded cumulative probabilities on an interactive standard bell curve.

Presets:

Parameters

Z-Score
+1.0000
Standard score
P(Z < z) Left
0.8413
84.13% Percentile
P(Z > z) Right
0.1587
15.87% Above
Two-Tailed P
0.3173
p-value (2-tail)

๐Ÿ”” Standard Normal Distribution Bell Curve (N(0, 1))

Shaded: P(Z < 1.00)

๐Ÿ“ Statistical Step-by-Step Derivation

Formula & Definition of Z-Score

The standard score, or Z-score, is the number of standard deviations by which the value of a raw score x is above or below the mean value of what is being observed. The formula is:

Z = (X - ฮผ) / ฯƒ

For samples with sample mean xฬ„ and sample standard deviation s, the formula is equivalently Z = (X - xฬ„) / s.

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