In a certain year, when she was a high school senior, Idonna scored 666 on the m
ID: 3206127 • Letter: I
Question
In a certain year, when she was a high school senior, Idonna scored 666 on the mathematics part of the SAT. The distribution of SAT math scores in that year was Normal with mean 523 and standard deviation 121 .
Jonathan took the ACT and scored 27 on the mathematics portion.
ACT math scores for the same year were Normally distributed with mean 20.9 and standard deviation 5.4 .
Find the standardized scores (± ± 0.01) for both students.
Assuming that both tests measure the same kind of ability, who had the higher score? Idonna's standardized score is Jonathan's standardized score is Idonna's score is less than Jonathan's Scores are equal Idonna's score is higher than Jonathan's
Explanation / Answer
Z = (X - mean) / sd
Z-score for Idonna score of 666 = (666 - 523) / 121 = 1.18
Z-score for Jonathan score of 27 = (27 - 20.9) / 5.4 = 1.13
So, Idonna had the higher score.
Idonna's standardized score is more than Jonathan's standardized score