Eevee from Period 1 got 86, while Harley from Period 2 got 90. Who did better on the test in relation to their class? Explain your answer

Question

Two statistics classes took a test. Period 1 had an average test score of 77 and a standard deviation of 6. Period 2 had an average test score of 81 and a standard deviation of 5. Eevee from Period 1 got 86, while Harley from Period 2 got 90. Who did better on the test in relation to their class? Explain your answer. *

Answer 1

We need to determine the percentile for each student's score from probabilities looked up from the standard normal probability table.

z-score is (x - mean)/standard deviation (SD), where x is individual student test score and is used to look up associated probabilities in standard normal probability table.

for Eevee from Period 1, x = 86, mean = 77 and (SD) = 6

and z = (86-77)/6 = 1.5.

From the standard normal probability table, a z-score of 1.5 corresponds to a probability of 0.9332, which translates to a percentile of 93.32%

for Harvey from Period 2, x = 90, mean = 81 and (SD) = 5

and z = (90-81)/5 = 1.8.

From the standard normal probability table, a z-score of 1.8 corresponds to a probability of 0.9641, which translates to a percentile of 96.41%

Thus, Harvey did better in relation to his class.