The normal distribution, often called the bell curve, is a symmetric, bell-shaped probability distribution widely used to model natural variability and measurement errors.

Characterized by its mean μ and standard deviation σ, it peaks at the mean and tapers off symmetrically on both sides.

It appears frequently in natural settings because averaging many small, independent effects tends to produce results that cluster around a central value, naturally forming a bell-shaped distribution.

We say that X follows a normal distribution, or X∼N(μ,σ).

The probability that X is less than a given value a, written P(X<a), is equal to the area under the curve to the left of x=a:

It follows that the total area under the curve is 1, which is required as the probabilities must sum to 1.