---
title: "Normal approximation to the Student-t distribution"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575269/Normal%20approximation%20to%20the%20Student-t%20distribution"
format: markdown
---
The [Student-t](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575254/) distribution, Student(0,1,*n*) or Student(*n*), is quite difficult to calculate, but when *n* is large it is well approximated by a [Normal](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575246/) distribution, as follows:

 

Student(*n*) » Normal(0, 1)

 

A general rule for this approximation is that *n* > 30. The relationship between the [Student-t](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575254/) and [Normal](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575246/) distributions is not intuitively obvious, but is readily made apparent by doing a Taylor series expansion about *x* = 0 of the probability density function for the Student distribution.

 

![image](media://b541a68a-bdd0-431d-98dc-29d108f53360)

 

 

 

---