Result
Enter values and select Calculate.
Formula and methodology
Values are standardized with z = (x − μ) / σ. Interval probability is Φ(z₂) − Φ(z₁); outside probability is Φ(z₁) + 1 − Φ(z₂).
Worked example
For a standard normal distribution, P(−1 ≤ Z ≤ 1) is approximately 0.6826894921.
Assumptions and interpretation
- Inputs and results remain in this browser and are not sent to analytics.
- This tool performs general educational statistical computation; it does not select a study design or validate scientific conclusions.
- Confidence-interval coverage describes repeated use of the method under its assumptions, not a probability assigned to the fixed parameter after calculation.
- Keep full precision for decisions; displayed values are rounded for readability.