The Normal Probability Distribution

Definition: If a continuous random variable has a probability distribution with a graph that is symmetric and bell-shaped, and it can be described by the function equation

$$ f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2} \quad\quad -\infty \leq x \leq \infty $$

then we say it has a normal distribution.