I understand that $$\sqrt{n}(\frac{\bar{X} - \mu}{\sigma})$$
has a standard normal distribution, as per definition.
How do I approximate this distribution to the t distribution? According to my tutor, this approximates to the t distribution with (n-1) degrees of freedom. And the equation will look like this.
$$\frac{\sqrt{n}(\bar{X} - \mu)}{s}$$
The only theorem I can think of that fits into this situation is that if Z~N(0,1) and U~$X_n^2$ and Z and U are independent, then the distribution of $\frac{Z}{\sqrt{U/n}}$ will be the t distribution with n degrees of freedom.