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

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.

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