I will be teaching the normal distribution in January and I need to know how to effectively explain the concepts that does not in any way confuse students or make them feel that the material is arbitrary.
How can I explain this formula to high school students?:
$f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{ -\frac{(x-\mu)^2}{2\sigma^2} }$
They do know the pmf for binomial distributions though they don't know the vocabularly "pmf" or "pdf"