The mean starting salary of college grads is $\$45,800$. The population is skewed right with an SD of $\$9,100$.
What is the probability of $36$ randomly selected college grads having a mean starting salary less than $\$45,000$.
I know how to use a $z$ table. I'm just unsure of how to solve the problem when there is a given ($36$) sample size.
Hint:
If $$X_i\sim\mathrm{N}(\mu,\sigma^2)$$ i.e. $X_i$ follows normal distribution with mean $\mu$ and variance $\sigma^2$ then $$\frac{\sum_{1\le i\le n}X_i}{n}=\overline{X_{n}}\sim\mathrm{N}\left(\mu,\frac{\sigma^2}{n}\right)$$ i.e mean of a sample of independent $X$'s with size of $n$, $\overline{X_{n}}$, follows normal distribution with mean $\mu$ and variance $\displaystyle\frac{\sigma^2}{n}=\left(\frac{\sigma}{\sqrt n}\right)^2$
You can prove this easily by considering $E\left[\overline{X}\right]$ and $\mathrm{Var}\left[\overline{X}\right]$