Normal Distribution Calculator

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Normal Distribution Calculator

This Normal Distribution Calculator computes Z-scores, probabilities, and raw scores (X-values) for any normally distributed dataset, aiding in data analysis and interpretation.

Normal Distribution Calculator

Enter distribution values, choose a normal query, then compute to see the selected result, interpretation, curve, and related values.

Show Formula & Example

Convert X to Z

Standardizing tells how many standard deviations an observed value is from the mean.

z = (X - μ) / σ

Subtract the mean from the observed value.
Divide by the standard deviation.
A positive z is above the mean; a negative z is below it.

Generic Example

If X = 85, μ = 70, and σ = 10, then z = (85 - 70) / 10 = 1.5.

The example is generic and does not use the values entered above.

Related Calculators:

Hypothesis Test Poisson Distribution Binomial Distribution

Calculator Resources

This section provides essential information and guidance to help you make the most of the calculator.

What is a Normal Distribution?

The normal distribution, often referred to as the bell curve, is a fundamental concept in statistics and probability theory. It describes how data points are distributed around a central value, with most observations clustering near the mean and fewer observations appearing as one moves further away from the mean.

The normal distribution is characterized by two parameters: the mean ($\mu$), which determines the center of the distribution, and the standard deviation ($\sigma$), which dictates the spread or variability of the data. This distribution is ubiquitous, appearing in natural phenomena (e.g., human height, blood pressure), measurement errors, and as an approximation for many other probability distributions.

Purpose of the Calculator

This Normal Distribution Calculator is a versatile online tool designed to simplify complex calculations related to the normal distribution. It allows users to compute probabilities (areas under the curve), convert X-values to Z-scores, find X-values corresponding to specific Z-scores, and determine Z-scores and X-values for given probabilities (inverse normal calculations), all while visualizing the distribution.