The grades on a history midterm at Almond are roughly symmetric wi
μ = 81 and σ = 2.5.
Luis scored 84 on the exam.
Find the z-score for Luis's exam grade. Round to two decimal places.



Answer :

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.