Normal distribution & z-scores
Probabilities below, above or between values, and the value at any percentile.
The average of the distribution.
How spread out the values are; above 0.
The value x to find the probability for.
Probability97.50%As a decimal: 0.9750
z-score1.96
Same results as Excel's NORM.DIST(x, μ, σ, TRUE) and NORM.INV(p, μ, σ).
About this calculator
Find probabilities for a normal distribution with any mean and standard deviation: the area below a value, above it, or between two values, and the value at a given percentile. It replaces a printed z-table.
Formula
z = x − μσ
- For the standard normal, P(Z ≤ 1.96) ≈ 0.975, so 95% of values lie within ±1.96σ.
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