Question

On a standardized exam, the scores are normally distributed with a mean of 75 and astandard deviation of 10. Find the z-score of a person who scored 105 on the exam.

Answer 1

The standard Z-score is given by the equation:

`\begin{gathered} Z=(x-\mu)/(\sigma) \\ \text{where '}\mu^(\prime)\text{ represents the mean} \\ \text{'}\sigma^(\prime)\text{ represents the standard variation} \\ ^(\prime)x^(\prime)\text{ represent the observed value} \end{gathered}`
`\begin{gathered} Z=(105-75)/(10) \\ Z=(30)/(10) \\ Z=3 \end{gathered}`

Hence, the Z-score is 3