Elementary Statistics: Picturing the World (6th Edition)

Published by Pearson
ISBN 10: 0-32191-121-0
ISBN 13: 978-0-32191-121-6

Chapter 5 - Normal Probability Distributions - Section 5.3 Normal Distributions: Finding Values - Exercises - Page 258: 31

Answer

a) $x \approx$ 68.96 inches b) $x \approx$ 62.26 inches

Work Step by Step

$\mu$ = 64.2, $\sigma$ = 2.9 Part A 1) Find the z score that corresponds to an area of 0.95: z = 1.64 2) Sub the values in z = $\frac{x - \mu}{\sigma}$ and solve for $x$ z = $\frac{x - 64.2}{2.9}$ $1.64$ = $\frac{x - 64.2}{2.9}$ $x$ = $1.64(2.9) + 64.2$ $x$ $\approx$ 68.96 inches Part B 1) Find the z score that corresponds to an area of 0.25: z = -0.67 2) Sub the values in z = $\frac{x - \mu}{\sigma}$ and solve for $x$ z = $\frac{x - 64.2}{2.9}$ $-0.67$ = $\frac{x - 64.2}{2.9}$ $x$ = $-0.67(2.9) + 64.2$ $x$ $\approx$ 62.26 inches
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