On a standardized exam, the scores are normally distributed with a mean of 250 and a standard deviation of 20. Find the z-score of person who scored 310 on the exam.
To find the z-score, we can use the formula:
\[ z = \frac{x - \mu}{\sigma} \]
where:
- \( x = 310 \) (the score)
- \( \mu = 250 \) (the mean)
- \( \sigma = 20 \) (the standard deviation)
Plugging the values into the formula:
\[ z = \frac{310 - 250}{20} = \frac{60}{20} = 3 \]
Therefore, the z-score of a person who scored 310 on the exam is 3.