Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 6 - Normal Probability Distributions - 6-3 Applications of Normal Distributions - Basic Skills and Concepts - Page 269: 26


a) $23.32$ inches b) This works for most people.

Work Step by Step

a) We can find that the z-score that corresponds to this is $1.6$. Hence, it follows: $(1.6)(1.2)+21.4=23.32.$ Women are generally shorter, so when determining the minimum height, we do not have to worry about the height of women. b. We find the z-scores for the genders: $z_{men}=\frac{23.5−21.4}{1.2}=1.75$ $z_{women}=\frac{23.5−19.6}{1.1}=3.55$. Using a z-table, we can see that more than $95$ percent of men and around $99.99$ percent of women will fit, so this works for most people.
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