Normal distribution: Symmetric intervals

It may be interesting to familiarize ourselves with the probabilities correspondig to different intervals in normal distributions.

Probability for an Interval = Area under the density curve in that interval

On the basis of a probability density function, you can calculate the probability that the random variable falls within a given range by estimating the area under the curve for that range. With the cumulative probability function you can do the same, but then more accurately

Two points on the x-axis determine the extremes of the interval for which the probability is calculated (approximately)

Different options A1, A2, ..., A6 correspond to different intervals that can be defined with those two points. Taken in pairs these are complementary in the sense that the sum of probabilities is 1.

We can modify the parameters of the normal distribution and see how the probabilities vary.

The red dots control vertical and horizontal scales of the graphic.

REFERENCES

George Marsaglia's article Evaluating the Normal Distribution.