Calling stats experts ofr a question regarding z table and normal distribution

[caribeaz]

A beginner question but I would like to understand this. I'm studying normal distribution and probability and would like to know where the values in the [z table](https://www.ztable.net) come from and how they are calculated. All sites I see just link to the table but none show how the values originate.

P.S. Also forgot how to add a link properly. Can someone show me how it's done

[HelloNurse]

For a definition of what the tables are about see the example on that site, it's worded casually but actually formal and precise. The values are obtained by computing integrals to find the area under a portion of the Gaussian curve (negative infinity to z or z to positive infinity). These particular integrals are traditionally called error functions.

[caribeaz]

Umm..can you ELI5 this a bit for me?

[HelloNurse]

Given a random variable x with a Gaussian probability distribution function of mean µ and standard deviation σ, we can normalize it by considering a transformed, and also Gaussian, random variable z=(x-µ)/σ with mean 0 and standard deviation 1.

The table gives the probability that z is lower than the given number; as you can see, values lower than -4 or greater than +4 aren't interesting.

Regarding the values, study calculus and you will be enlightened. Sorry, there is no shortcut.

[caribeaz]

So links in text posts don't get parsed..if I am correct? But they do in comments? Let me try this https://www.ztable.net

Edit: It works.