Elementary Statistics: A Step-by-Step Approach with Formula Card 9th Edition

Published by McGraw-Hill Education
ISBN 10: 0078136334
ISBN 13: 978-0-07813-633-7

Chapter 3 - Data Description - 3-3 Measures of Position - Extending the Concepts - Page 161: 33


Tom, Harry, Dick.

Work Step by Step

Given $\mu=125$ and $\sigma=18$ Tom $x=158$ Harry $z=2.00$, $\frac{x-125}{18}=2$, $x=161$ Dick 98th percentile, empirical rule states that $95\%$ fall within $z=-2, and +2$, so $z=2$ is at 97.5th (95+5/2) percentile. This means that 98th percentile is better than $z=2$ (this can be confirmed by using a z-table) The ranks are: Tom, Harry, Dick.
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