On a standardized exam, the scores are normally distributed with a mean of 700 and a standard deviation of 100. Find the z-score of a person who scored 675 on the exam.
To find the z-score of a person who scored 675 on the exam, we use the formula:
\[ z = \frac{X - \mu}{\sigma} \]
Where:
- \(X\) is the person's score (675)
- \(\mu\) is the mean (700)
- \(\sigma\) is the standard deviation (100)
Plugging in the values, we get:
\[ z = \frac{675 - 700}{100} = \frac{-25}{100} = -0.25 \]
Therefore, the z-score of a person who scored 675 on the exam is -0.25.