The Basic Practice of Statistics 7th Edition

Published by W. H. Freeman
ISBN 10: 1-46414-253-X
ISBN 13: 978-1-46414-253-6

Chapter 3 - The Normal Distributions - Apply Your Knowledge: 3.8

Answer

Standardized score for Idonna's SAT math score: 1.32 Standardized score for Jonathan's ACT math score: .96 Idonna's standardized score is higher, so assuming both tests measure the same kind of ability, Idonna's score is higher.

Work Step by Step

We can use the standardized normal distribution to calculate a standardized score (z-score) that allows us to compare values from two different normal distributions. The z-score is calculated as $z = (x-µ) \div σ$ x is an observation, µ is the mean of the distribution, σ is the standard deviation of the distribution z-score for Idonna = $(670-514) \div 118 = 1.32$ z-score for Jonathan = $(26-20.9) \div 5.3 = .96$
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