To compare the students' scores, we need to standardize them by using the z-score formula, which is:
z = (x - #) / #
where x is the raw score, # is the mean, and # 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.
References: Comparing with z-scores (video) | Z-scores | Khan Academy, 17 Important Data Visualization Techniques | HBS Online