stats

Normal Distribution

Z-score, PDF, CDF, tail areas, and shaded bell curve for any μ, σ, and X.

Input Mode

Mean μ

Std Dev σ

Target Value X

Results

Z-Score—

PDF at X φ(x)—

CDF — P(X ≤ x)—

Right tail — P(X > x)—

Between μ and X—

Z = (X−μ)/σ · Φ(z) = ½(1+erf(z/√2)) · A&S 7.1.26

CDF approximation max error: 1.5 × 10⁻⁷
Z lookup: enter any Z, get Φ(z) directly.