Free Normal Distribution Calculator
Calculate the probability density function (PDF) value and key properties of the normal distribution for a given x, mean, and standard deviation.
Z-Score
0.500000
PDF f(x)0.03520653
Deviations from Mean0.5000
Variance100.0000
Z-Score vs Value (x)
How to Use the Normal Distribution
PDF Formula
f(x) = (1 / (sigma * sqrt(2*pi))) * e^(-0.5 * ((x - mu)/sigma)^2)
The normal (Gaussian) distribution is the most important continuous distribution in statistics. It is defined by its mean (mu) and standard deviation (sigma). The z-score standardizes any value to units of standard deviations from the mean.
Example Calculation
Test scores have mean 70 and SD 10. Find the z-score and PDF for a score of 75.
- 01Z = (75 - 70) / 10 = 0.5
- 02The score is 0.5 standard deviations above the mean
- 03PDF = (1 / (10 * sqrt(2*pi))) * e^(-0.5 * 0.25)
- 04= 0.03989 * 0.8825 = 0.03521
- 05Variance = 10^2 = 100
Frequently Asked Questions
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Understanding the Normal Distribution
Learn what the normal distribution is, why it matters in statistics, and how to use the bell curve for probability calculations, z-scores, and real-world data analysis.