Question

In a statistic examination, the mean was 55 and the standard deviation was 10. Determine the standard scores of two students whose grade were 75 and 42 respectively.

Answer 1

$$z=\dfrac{x-\mu}{\sigma}$$

Given $\mu=55, \sigma=10$

$$x=75: z=\dfrac{75-55}{10}=2$$

$$x=42: z=\dfrac{42-55}{10}=-1.3$$