On a standardized exam, the scores are normally distributed with a mean of 700 and a standard deviation of 20. Find the z-score of a person who scored 705 on the exam.
To find the z-score of a person who scored 705 on the exam, we use the formula:
\[ z = \frac{X - \mu}{\sigma} \]
where:
- \(X\) is the score of the person (705)
- \(\mu\) is the mean (700)
- \(\sigma\) is the standard deviation (20)
Plugging in the values, we get:
\[ z = \frac{705 - 700}{20} \]
\[ z = \frac{5}{20} \]
\[ z = 0.25 \]
Therefore, the z-score of a person who scored 705 on the exam is 0.25.