Sampling Distribution

Question

Suppose $X \sim N(\mu, \sigma^2)$. After $n$ independent draws $\bar{X} \sim N(\mu, \frac{\sigma^{2}}{n})$. I am assuming that each draw contains $n$ numbers? Because if each draw only had one number then we would only have one mean.

Answer 1

You are assuming the $i$-th draw, denoted by $X_i$, is one number. $\bar{X}$ is defined to be $\frac{1}{n}\sum_{i=1}^n X_i$: you have one mean for the entire sample $X_1,\ldots,X_n$.