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