Normal distribution calculator

Enter the mean μ (average), standard deviation σ, and cutoff points, and this normal distribution calculator will compute the area (probability) under the normal distribution curve.

Enter the parameters of the normal distribution:

μ

σ

Above

Below

Between

and

Outside

and

Result:

μ = 16.5
σ = 8.4013887740857

Area (probability) = 0

The normal distribution, also known as the Gaussian distribution, is a symmetric, bell-shaped curve that describes the distribution of many natural phenomena. It is characterized by its mean (μ or m) and standard deviation (σ or SD), which determine its center and spread, respectively.

In a normal distribution, about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations - three sigma rule.

The curve is perfectly symmetrical, with the mean, median, and mode all located at the center of the distribution. The tails of the normal distribution extend infinitely in both directions, but the probability of extreme values decreases rapidly.


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