Question

Apply Your Knowledge 3.8 from The Basic Practice of Statistics, 7^th Edition, by David S. Moore, William I. Notz, and Michael A. Fligner, 2015: In 2013, when she was a high school senior, Idonna scored 670 on the mathematics part of the SAT. The distribution of SAT math scores in 2013 was normal with mean 514 and standard deviation 118. Jonathan took the ACT and scored 26 on the mathematics portion. ACT math scores for 2013 were normally distributed with mean 20.9 and standard deviation 5.3. Find the standardized scores for both students. Assuming that both tests measure the same kind of ability, who had the higher score?

Answer 1

Solution:
Given in the question
Idonna scored on Mathematics part of the SAT = 670
Mean of SAT score = 514
The standard deviation of SAT score = 118
Standardized score for Iddona Z = (X - mean)/Standard deviation = (670-514)/118 = 1.32
Jonathan ACT score on mathematics portion = 26
Mean = 20.9
Standard deviation = 5.3
So Standardized score for Janathan Z = (26-20.9)/5.3 = 0.96
According to Z-scores, Idonna had higher score.