The Normal Distribution, also known as the Gaussian Distribution, is a symmetric, bell-shaped probability distribution that describes how values are distributed around the mean. It is widely used in statistics, natural sciences, and social sciences due to its applicability in real-world data.
\[ f(x) = \frac{1}{\sigma \sqrt{2\pi}} \, e^{ -\frac{(x - \mu)^2}{2\sigma^2} } \]
\[ F(x) = \int_{-\infty}^{x} \frac{1}{\sigma \sqrt{2\pi}} \, e^{ -\frac{(t - \mu)^2}{2\sigma^2} } \, dt \]