Continuous probability distribution
Standard Normal (Z) distribution
Z ~ Normal(0, 1)
The Normal distribution with mean 0 and standard deviation 1. Any Normal variable becomes standard via the z-score transform Z = (X − μ) / σ, which is how probability tables and critical values are built.
Explore it interactivelyKey facts
- Notation
- Z ~ Normal(0, 1)
- Type
- continuous
- Parameters
- — — no parameters (μ = 0, σ = 1)
- Support
- (−∞, ∞)
- φ(z) = 1 / √(2π) · e^(−z² / 2)
- Mean
- 0
- Variance
- 1
When to use it
- Computing z-scores
- Standardising data before comparison
- Critical values for hypothesis tests
- Reading Normal probability tables
Related distributions
Frequently asked questions
What is the Standard Normal (Z) distribution?
The Normal distribution with mean 0 and standard deviation 1. Any Normal variable becomes standard via the z-score transform Z = (X − μ) / σ, which is how probability tables and critical values are built.
What are the mean and variance of the Standard Normal (Z) distribution?
For Z ~ Normal(0, 1), the mean is 0 and the variance is 1.
When is the Standard Normal (Z) distribution used?
It is commonly used for: Computing z-scores; Standardising data before comparison; Critical values for hypothesis tests; Reading Normal probability tables.
All distribution guides
BernoulliBinomialPoissonDiscrete UniformContinuous UniformNormal (Gaussian)Standard Normal (Z)ExponentialChi-squared (χ²)F (Fisher–Snedecor)
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