Probabilities under normal curves or any shape probability distribution function are measured as areas under the curve. It helps to have an integral calculus intuition for comparing p(0.1<x<0.5) to p(0.5<x<0.6). It helps to have a multi variate vector distance interpretation of length for error and variance magnitude.

> Yes, a statistics course is so much more useful. It's not emphasized in school but it will truly help through out your life if you understand it.

I think this may be based on an impression of what math coursework used to be. A statistics course is a very common, if not required, part of any modern mathematics major.