About this tool: Normal Distribution Probability
Find probabilities between two bounds of a normal distribution using the mean and positive standard deviation.
Enter the mean, a strictly positive standard deviation and ordered bounds a≤b. The shaded curve is shown in standardized z coordinates over −4 to 4, while probabilities use the actual bounds. The numerical normal-tail approximation has absolute error below about 1.5×10⁻⁷; very small tails can underflow.
How the calculation works
Worked example
| Mean | 0 |
| σ | 1 |
| a | -1 |
| b | 1 |
P(−1≤X≤1) ≈ 0.68268949
Questions and answers
What does this tool do?
Find probabilities between two bounds of a normal distribution using the mean and positive standard deviation. Enter the mean, a strictly positive standard deviation and ordered bounds a≤b. The shaded curve is shown in standardized z coordinates over −4 to 4, while probabilities use the actual bounds. The numerical normal-tail approximation has absolute error below about 1.5×10⁻⁷; very small tails can underflow.
What affects precision and input format?
Normal probabilities use a numerical approximation with absolute error about 1.5×10⁻⁷ or less.
Where are the calculations performed?
The calculation runs in your browser. You can use the tool without installing software.
Asted Cloud
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