Introduction to the Normal (Gaussian) Distribution
The normal distribution, also known as the Gaussian distribution or the bell curve, is the most important probability distribution in statistics. It describes a continuous probability distribution that is symmetrical about its mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a bell-shaped curve. This distribution is ubiquitous because of the Central Limit Theorem, which states that the sum of many independent and identically distributed random variables tends toward a normal distribution, regardless of their original distribution.
Many natural phenomena and human measurements closely follow a normal distribution. Examples include height, weight, blood pressure, IQ scores, standardized test results, and measurement errors in scientific experiments. Because of its predictable mathematical properties, scientists and statisticians use the normal distribution to perform hypothesis testing, calculate confidence intervals, and estimate population parameters from sample data.
This calculator allows you to define any custom normal distribution by entering its mean $\mu$ and standard devation $\sigma$. It computes the probability of obtaining values below, above, or between specific thresholds, converts values to standard Z-scores, and generates an interactive, shaded bell curve visualization.