To determine who performed better on the exam relative to their class, we can use z-scores. A z-score measures how many standard deviations a data point is from the mean.
For Joey:
Z-score = (Joey's score - Joey's class mean) / Joey's class standard deviation
Z-score = (88 - 86) / 4
Z-score = 0.5
For Jesse:
Z-score = (Jesse's score - Jesse's class mean) / Jesse's class standard deviation
Z-score = (88 - 84) / 3
Z-score = 1.33
A higher z-score indicates a better performance relative to the class. In this case, Jesse had a higher z-score of 1.33 compared to Joey's z-score of 0.5, which means Jesse performed better relative to their respective classes.