Normal Distribution

Bell curve PDF and CDF with shaded probabilities

X ~ N(μ = 0, σ = 1) · P(X ≤ 1)
P(X ≤ x) — left tail
0.841345
z-score
1
Density f(x)
0.241971
Percentile
84.1345
P(X ≤ x)
0.841345
P(X ≥ x)
0.158655
Bell curve with the selected probability region shaded. P(X ≤ 1) = 0.841345Bell curve with the selected probability region shaded. P(X ≤ 1) = 0.841345xf(x)-4-3-2-112340.10.20.30.4

この計算機について

The Normal Distribution Calculator draws the bell curve for any mean and standard deviation and shades the probability you choose — the left tail P(X ≤ x), the right tail P(X ≥ x), or the area between two bounds P(a ≤ X ≤ b). It also reports the density f(x), the z-score, and the percentile. Useful for statistics, z-scores, hypothesis testing, and exam grading.

一般的な例

  • Standard normal N(0, 1): P(Z ≤ 1) = 0.8413 (84th percentile)
  • Right tail P(Z ≥ 1.5) = 0.0668
  • One-sigma rule: P(−1 ≤ Z ≤ 1) = 0.6827
  • Two-sigma rule: P(−2 ≤ Z ≤ 2) = 0.9545
  • IQ scores N(100, 15²): P(X ≤ 130) = 0.9772 (z = 2)