Kaitlyn and Allison took a standardized algebra test in different states. Kaitlyn took the test for Virginia and scores a 458 Allison took the test for North Carolina and scored a 185 Suppose the mean and standard deviation for the algebra scores for Virginia were 405 and 30 , respectively, and the mean and standard deviation for the algebra scores for North Carolina were 152 and 20 , respectively. Which student did better on her algebra test?
Answer
A
Allison did better since her z -score is higher than Kaitlyn’s z -score.
B
Kaitlyn did better since her z -score is higher than Allison’s z -score.
C
Allison did better since her z -score is closer to the mean than Kaitlyn’s z -score.
D
Kaitlyn and Allison did equally well since their scores are both above the mean.
Explanation
Compare their z-scores, which show how many standard deviations each score is above its state’s mean. Kaitlyn’s z-score is (458 − 405) ÷ 30 ≈ 1.77, while Allison’s is (185 − 152) ÷ 20 = 1.65. Kaitlyn’s score is farther above her state’s average, so Kaitlyn did better; the correct choice is B, “Kaitlyn did better since her z-score is higher than Allison’s z-score.”
AI-written and checked against the verified answer.