# What is the z-score of X, if n = 204, mu= 15, SD =1, and X =35?

$z = \frac{X - \mu}{S D} = \frac{35 - 15}{1} = 20$ is the $z$-score of $X$ itself. If you want the $z$-score of a mean $\overline{X} = 35$, the answer is $z = \frac{\overline{X} - \mu}{\frac{S D}{\sqrt{n}}} = \frac{20}{\frac{1}{\sqrt{204}}} \approx 285.7$. Such high $z$-scores rarely occur in real life examples.