Normal Distribution

$\quad N(\mu, \sigma^2)$

Normal Distribution Calculator
Statistics » Linear Correlation » Binomial » Regression » Statistics and Probability

The Normal Distribution

The normal distribution, or "bell curve," is a fundamental concept in statistics. It's a symmetric probability distribution described by its mean ($\mu$) and standard deviation ($\sigma$). This toolkit allows you to calculate probabilities and test if your own data follows a normal pattern.

Key Concepts:

Z-score: A Z-score, calculated as $Z = (X - \mu) / \sigma$, measures how many standard deviations a value $X$ is from the mean.
Empirical Rule: For a normal distribution, approximately 68% of data falls within $\pm 1\sigma$, 95% within $\pm 2\sigma$, and 99.7% within $\pm 3\sigma$ of the mean.

Normal Probability Calculator

Mean ($\mu$):

Std. Dev. ($\sigma$):

Value $X_1$ (or Z-score if $\mu=0, \sigma=1$):

Value $X_2$ (optional, for range):

Inverse Normal Calculator

Find the X or Z value for a given cumulative probability (area to the left).

Mean ($\mu$):

Std. Dev. ($\sigma$):

Area to the left $P(X < x)$:

Test for Normality

Enter your own data to see its descriptive statistics and check if it follows a normal pattern.

Enter Data (comma-separated):

Histogram Bins (optional):