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Normal distribution calculator

The probability that a normally distributed value falls below, above or between two values.

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Results

Between a and b 77.45%

How it works

P(a < X < b) = Φ((b − μ) ÷ σ) − Φ((a − μ) ÷ σ)

Heights, test scores and measurement errors often follow a bell curve. Turn each limit into a z-score, look up the area under the curve to its left (Φ), and subtract. About 68% of values lie within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3.

  1. Z-scores of the limits (160 − 170) ÷ 10 = -1 · (185 − 170) ÷ 10 = 1.5
  2. Area between them Φ(1.5) − Φ(-1) = 77.45%

Printed from rocketcalc.io/math/normal-distribution