To find the z-score for Luis's exam grade, we can use the formula:
\[ z = \dfrac{x - \mu}{\sigma} \]
where:
- \( x \) is Luis's exam grade (84)
- \( \mu \) is the mean exam grade (81)
- \( \sigma \) is the standard deviation (2.5)
Substitute the values into the formula:
\[ z = \dfrac{84 - 81}{2.5} \]
\[ z = \dfrac{3}{2.5} \]
\[ z = 1.2 \]
Therefore, Luis's z-score for the exam grade is 1.20 when rounded to two decimal places. This means that Luis's exam grade is 1.20 standard deviations above the mean grade.
