If a random sample of size $n$ is drawn from a population that is exactly normal with mean $\mu$ and variance ${\sigma }^2$, which statement is correct about the sampling distribution of the sample mean $\bar{X}$?

$\bar{X}$ is approximately normal only for large $n$.

$\bar{X}$ is exactly normal for any $n$ and has distribution $N(\mu ,\frac{{\sigma }^2}{n})$.

$\bar{X}$ follows a Student's $t$-distribution with $n-1$ degrees of freedom.

$\bar{X}$ is exactly normal with variance ${\sigma }^2$.