91Ó°ÊÓ

$\begin{array}{c}\text{z-scorefor0=}\frac{\text{Value}−\mathrm{μ}}{\text{σ}}\\ =\frac{0−2}{1}\\ =−2\end{array}$

$\begin{array}{c}\text{z-scorefor4=}\frac{\text{Value}−\text{μ}}{\text{σ}}\\ \text{=}\frac{\text{4}−\text{2}}{\text{1}}\\ \text{=2}\end{array}$

$\begin{array}{c}\text{z-scorefor12=}\frac{\text{Value}−\mathrm{μ}}{\text{σ}}\\ \text{=}\frac{\text{12}−\text{2}}{\text{1}}\\ \text{=10}\end{array}$

When the mean is 2 and the standard deviation is 1, z- scores for 0, 4, 12 are -2, 2, 10 respectively.

$\begin{array}{c}\text{z-scorefor0=}\frac{\text{Value}−\mathrm{μ}}{\text{σ}}\\ \text{=}\frac{\text{0}−\text{4}}{\text{2}}\\ \text{=}−\text{2}\end{array}$

$\begin{array}{c}\text{z-scorefor4=}\frac{\text{Value}−\mathrm{μ}}{\text{σ}}\\ \text{=}\frac{\text{4}−\text{4}}{\text{2}}\\ \text{=0}\end{array}$

$\begin{array}{c}\text{z-scorefor12=}\frac{\text{Value}−\mathrm{μ}}{\text{σ}}\\ \text{=}\frac{\text{12}−\text{4}}{\text{2}}\\ \text{=4}\end{array}$

When the mean is 4 and the standard deviation is 2, the z-scores for 0, 4, and 12 are -2, 0, and 4 respectively.

$\begin{array}{c}\text{z-scorefor0=}\frac{\text{Value}−\text{μ}}{\text{σ}}\\ \text{=}\frac{\text{0}−\text{8}}{\text{2}}\\ \text{=}−\text{4}\end{array}$

$\begin{array}{c}\text{z-scorefor4=}\frac{\text{Value}−\text{μ}}{\text{σ}}\\ \text{=}\frac{\text{4}−\text{8}}{\text{2}}\\ \text{=}−\text{2}\end{array}$

$\begin{array}{c}\text{z-scorefor12=}\frac{\text{Value}−\text{μ}}{\text{σ}}\\ \text{=}\frac{\text{12}−\text{8}}{\text{2}}\\ \text{=2}\end{array}$

Here the z-scores are 0 = -4, 4 = -2, 12 = 2.

$\begin{array}{c}\text{z-scorefor0=}\frac{\text{Value}−\text{μ}}{\text{σ}}\\ \text{=}\frac{\text{0}−\text{8}}{\text{8}}\\ \text{=}−\text{1}\end{array}$

$\begin{array}{c}\text{z-scorefor4=}\frac{\text{Value}−\text{μ}}{\text{σ}}\\ \text{=}\frac{\text{4}−\text{8}}{\text{8}}\\ \text{=}−\text{0.5}\end{array}$

$\begin{array}{c}\text{z-scorefor12=}\frac{\text{Value}−\text{μ}}{\text{σ}}\\ \text{=}\frac{\text{12}−\text{8}}{\text{8}}\\ \text{=0.5}\end{array}$

Therefore, the z-scores are -1, -0.5 and 0.5.