Analyze probabilities and densities of the most common statistical distribution.
Distribution Parameters
Probability Analysis
Cumulative Probability P(X ≤ x)90.25%Interpretation: Near Average
Z-Score1.000
PDF Density0.2420
μ ± 1σ
68.27%
μ ± 2σ
95.45%
μ ± 3σ
99.73%
About this calculator
Overview
The normal distribution, also known as the Gaussian distribution, is a symmetrical probability distribution that is central to the field of statistics. It is defined by its mean (middle of the curve) and standard deviation (spread of the curve).
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Pro Tips
Use the Z-score to determine how many standard deviations an observation is from the mean.
The cumulative probability tells you the percentile rank of your observation.
Ensure standard deviation is always greater than zero.
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Probability Density Function
The normal distribution's density function (Gaussian function) is defined by:
