# What is the z-score of X, if n = 3, mu= 55, SD =2, and X =56?

Mar 4, 2016

Z-score is $- 0.866$
z-score of variable $x$ with mean $\mu$, and standard deviation $\sigma$ is given by $\frac{x - \mu}{\frac{\sigma}{\sqrt{n}}}$
As $\mu = 55$, $\sigma = 2$, $n = 3$ and $x = 56$
z-score is $\frac{56 - 55}{\frac{2}{\sqrt{3}}} = \frac{\left(- 1\right) \cdot \sqrt{3}}{2} = - 0.866$