Question

On a standardized exam, the scores are normally distributed with a mean of 80 and a standard deviation of 20. Find the z-score of a person who scored 90 on the exam.

Answer 1

To find the z-score, you can use the formula:

\[ z = \frac{x - \mu}{\sigma} \]

Where:
- \( x = 90 \) (score of the person)
- \( \mu = 80 \) (mean of the exam scores)
- \( \sigma = 20 \) (standard deviation of the exam scores)

Plug in the values:

\[ z = \frac{90 - 80}{20} = \frac{10}{20} = 0.5 \]

Therefore, the z-score of a person who scored 90 on the exam is 0.5.