Normal Distribution Calculator
Find the probability that a normally distributed value falls below, above, between or outside given values.
P(X < a)
0.9750021049 (97.50021%)
- z for a
- 1.96
Show the work
Standardize a
z = (a − μ) ÷ σ
(1.96 − 0) ÷ 1 = 1.96
Area below z (standard normal)
P(X < a) = Φ(z)
Φ(1.96) = 0.9750021049 (97.50021%)
How it works
P(X < x) = Φ((x − μ) ÷ σ), with Φ(−z) = ½ erfc(z ÷ √2) from the complementary error function (Abramowitz & Stegun 7.1.6 and 7.1.14), accurate to every shown digit even far out in the tails
Questions
- How does the normal distribution calculator work?
- P(X < x) = Φ((x − μ) ÷ σ), with Φ(−z) = ½ erfc(z ÷ √2) from the complementary error function (Abramowitz & Stegun 7.1.6 and 7.1.14), accurate to every shown digit even far out in the tails.
- What do I need to enter?
- Mean (μ), Standard deviation (σ), Find, a, b. Optional fields can be left blank.
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