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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"

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Maybe working with standard normal first ; $\mu=0, \sigma=1$ first may help simplify. Still, this seems like a nice link: courses.ncssm.edu/math/Talks/PDFS/normal.pdf –  user99680 Dec 7 '13 at 20:25
My answer would be don't try. At least don't try to explain the formula, try to explain how to interpret its graph. I suspect once things get too complicated a lot of kids tune out. –  jgon Dec 7 '13 at 20:36
Why mess with the formula at all? It contributes nothing to the basic concepts. I suggest looking at the treatment in the classic Freedman, Pisani, & Purves, Statistics. –  Brian M. Scott Dec 7 '13 at 21:28
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