T table with infinity degrees of freedom

Question

why is z table the same as a t table with infinity degrees of freedom. For example as df for the T distribution goes to infinity it becomes z ( standard normal) distribution. Is this true and why is this so? Thanks

Answer 1

Here is an explanation. The $t$-distribution $T$ is equal to:

$$ \frac{Z}{\sqrt{\chi^2 (k)/k}} $$

where $Z$ is the standard normal distribution. It can be shown, from the law of large numbers, that as $k$ approaches infinity, $\chi^2(k)/k$ approaches 1. And there you have it.