For a normal random variable,
$$ X \sim N(\mu,\sigma^2) $$the probability density function is
$$ f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left[ -\frac{(x-\mu)^2}{2\sigma^2} \right]. $$Use the sliders below to explore how the mean $\mu$ and standard deviation $\sigma$ affect the probability density.