In a certain year, when she was a high school senior, Idonna scored 661 on the m
ID: 3156832 • Letter: I
Question
In a certain year, when she was a high school senior, Idonna scored 661 on the mathematics part of the SAT. The distribution of SAT math scores in that year was Normal with mean 516 and standard deviation 125. Jonathan took the ACT and scored 25 on the mathematics portion. ACT math scores for the same year were Normally distributed with mean 21.2 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 Scores are equal Idonna's score is higher than Jonathan's Idonna's score is less than Jonathan's
Explanation / Answer
Mathematics, Idonna scored
Mean ( u ) =516
Standard Deviation ( sd )=125
Normal Distribution = Z= X- u / sd ~ N(0,1)
P(X < 661) = (661-516)/125
= 145/125= 1.16
= P ( Z <1.16) From Standard Normal Table
= 0.877
Mathematics, Jonathan scored
Mean ( u ) =21.2
Standard Deviation ( sd )=5.4
Normal Distribution = Z= X- u / sd ~ N(0,1)
P(X < 21.2) = (21.2-21.2)/5.4
= 0/5.4= 0
= P ( Z <0) From Standard Normal Table
= 0.5
Idonna's score is higher than Jonathan's