# What is the z-score of X, if n = 72, mu= 137, SD =25, and X =13?

Mar 4, 2016

z-score is $- 42.087$
z-score of variable $x$ with mean $\mu$, and standard deviation $\sigma$ is given by $\frac{x - \mu}{\frac{\sigma}{\sqrt{n}}}$
As $\mu = 137$, $\sigma = 25$, $n = 72$ and $x = 13$
z-score is $\frac{13 - 137}{\frac{25}{\sqrt{72}}} = \frac{\left(- 124\right) \cdot \sqrt{72}}{25} = - 42.087$