Question

The grades on a language midterm at Loyola are roughly symmetric with p = 69 and o = 4.0. Vanessa scored 65 on the exam. Find the z-score for Vanessa's exam grade. Round to two decimal places.

Answer 1

The z-score for Vanessa's exam grade is -1

Here, we want to calculate Vanessa's z-score for her exam score

Mathematically, we can calculate the z-score using the formula;

`\begin{gathered} z-\text{score = }\frac{x\text{ - }\mu}{\sigma} \\ \\ \text{where x is the raw score which is 65 in this case} \\ \mu\text{ is the mean score which is 69 in this case} \\ \sigma\text{ is the standard deviation which is 4 in this case} \\ \\ \text{Substituting these values;} \\ \\ z-\text{score = }(65-69)/(4)\text{ = }(-4)/(4)\text{ = -1} \end{gathered}`