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Statistics

Normal Probability Calculator

Compute probability between two bounds in a normal distribution.

Last validated: 2026-02-14

Use this free online Normal Probability Calculator to return probabilities and quantiles for the normal distribution. It is useful for analysis, reporting, coursework, and experiment planning when you need quick statistical evidence without building a spreadsheet. The form focuses on Mean, Std dev, x1, x2 and returns Normal Probability Inputs, Result, so you can move from input to answer without setting up a spreadsheet or custom script. Run one realistic example, adjust the inputs, and compare how the result changes before you copy or share it. Treat the result as a statistical aid: sample quality, independence, distribution assumptions, and context still determine whether the conclusion is valid.

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Input Pattern

Enter values in the left panel, keep units explicit, run the calculation, then copy or share the result. Invalid fields are highlighted immediately.

Normal Probability Inputs

Result

z1: -1.000000

z2: 1.000000

P(x1 <= X <= x2): 0.68268949

How to use this tool

  1. Enter Mean, Std dev, x1, x2 for the normal probability calculator, keeping units, dates, or text format consistent with the form labels.
  2. Confirm sample size, ordering, and distribution assumptions before relying on the calculated result.
  3. Click "Run the tool" and review Normal Probability Inputs, Result for the primary output.
  4. Check the statistical assumptions and sample context before using the result in a report or decision.

Worked Example

Auto-generated from the tool's current default or entered inputs.

Example Inputs

  • Std dev: 15.0
  • X1: 85.0
  • X2: 115.0
  • Z1: -1.0
  • Z2: 1.0

Expected Outputs

  • Mean: 100
  • Std dev: 15
  • X1: 85
  • X2: 115

Interpretation

Confidence and limitations

Formula References

Assumptions

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