Request: Adder Naga teaches Maths

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He wished for an Adder Naga. In his own Sleeping Stories Universe (SSU), Adder Nagas are an intelligent race of Nagas who have great interest in maths and teach maths to other inhabitants of SSU. fav.me/d4qgjxv

This Adder Naga seems to teach some calculus, but also stochastics is possible, since the function f(x) describes the Gaussian Distribution.

The Gaussian Distribution is important to describe e.g the body height of a population. Imagine you are designing a car and you have to make the roof of the car heigh enough so most people fit in. But how to find the best height?

If you calculate the x-value of the maximum, you find the average body height of the population.

If you calculate also the second derivation of f(x) and determine the position of the two inflection points, you have calculated the range of the standard deviation of the Gaussian Distribution. The value of the integral between the two inflection points is about 0,683. Since the complete area under the graph is exactly 1, the standard deviation covers 68,3% of the complete area.

This also means, that the x-values of the two in inflection points mark the body heights, between which you will find 68,3% of the population.
Two times the standard deviation cover around 95% of the population.
Three times the stnadard deviation cover around 99% of the population.

Designers usually use two times the standard deviation when dertermining e.g. the height of a car.