Question

9. The widths of platinum samples manufactured at a factory are normally distributed, with a mean of 1.2 cm and a standard deviation of 0.2 cm. Find the z-scores that correspond to each of the following widths. Round your answers to the nearest hundredth, if necessary.(a) 1.8 cmz = (b) 0.4 cmz =

Answer 1

We will simply employ the z-score formulae to getting our solution. It goes thus:

$\begin{gathered} z=\frac{x-\bar{x}}{\sigma} \\ \text{Where:} \\ x=\text{datum considered} \\ \bar{x}=\operatorname{mean} \\ \sigma=S\tan dard\text{ deviation} \end{gathered}$

Therefore, the z-scores are:

$\begin{gathered} z=\frac{1.8-1.2}{0.2}=\frac{0.6}{0.2}=3 \\ \\ z=\frac{0.4-1.2}{0.2}=-\frac{0.8}{0.2}=-4 \end{gathered}$

The z-scores are:

a) 3

b) -4