Try describing in equations how the "bean machine" (http://en.wikipedia.org/wiki/File:Planche_de_Galton.jpg http://en.wikipedia.org/wiki/File:Planche_de_Galton.

Try describing in equations how the "bean machine" (http://en.wikipedia.org/wiki/File:Planche_de_Galton.jpg http://en.wikipedia.org/wiki/File:Planche_de_Galton.jpg) works (you just need knowledge of basic probability, and then some calculus when you go to actually deriving the functions), until you get to the mathematical derivation of the bell curve - it will give you a very "mechinistically intuitive" understanding of it if you can imagine it starting from a physical mechanical process -> idealized physical process -> mathematical model -> generalize the model as much as possible -> come back to the real world by applying the model to real world problems. It's weird how intuitive stats becomes when you see it as "just physics and math" and then distill the purest "abstract" model out of it in a way that it can be used generally and without knowledge of how it was derived (I know, in school you're taught to "apply probability and statistics in physics and engineering", not to "apply physics and math and engineering to understand statistics and probability" - but this way of turning you mind upside down in a way that is "kind of wrong" helps your intuition a lot).