To compare the students’ scores, we need to standardize them by using the z-score formula, which is:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation. The z-score tells us how

many standard deviations a score is above or below the mean. A higher z-score means a better score

relative to the average.

Using the table, we can calculate the z-scores for each student as follows:

Randy: z = (76 - 70) / 2 = 3 Katie: z = (86 - 80) / 3 = 2 Ralph: z = (80 - 75) / 2 = 2.5 Jean: z = (80 - 90) / 1

= -10

The student with the highest z-score is Randy, with a z-score of 3. This means that Randy scored 3

standard deviations above the mean in math, which is the best performance among the four

students. Therefore, the correct answer is A.

Reference: Comparing with z-scores (video) | Z-scores | Khan Academy, 17 Important Data

Visualization Techniques | HBS Online