Normal CDF Calculator
P(Z ≤ z) for standard normal.
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Formula
Φ(z) = ∫_{−∞}^{z} φ(t) dt
Uses Abramowitz & Stegun rational approximation for the standard normal cumulative distribution.
Worked example
Φ(1.96) ≈ 0.975 — the familiar two-tailed 95% critical value.
Where this can give the wrong answer
- Approximation error tiny for |z| < 6.
- Assumes exact normality of data.
- Heavy tails in finance violate normality.
FAQ
- For |z|=1.96, two-tailed p ≈ 0.05.