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: 32

Answer

a) $x$ = 73.112 inches b) $x$ = 67.46 inches

Work Step by Step

PART A i) Find the z-score that corresponds to 0.90 Using the standard normal distribution table/technology we obtain a value of 1.28 ii) Sub known values into z = $\frac{x - \mu}{\sigma}$ and solve for $x$ 1.28 = $\frac{x - 69.4}{2.9}$ $x$ = $69.4$ + $(1.28 \times 2.9)$ $x$ = 73.112 inches PART B i) Find the z-score that corresponds to 0.25 Using the standard normal distribution table/technology we obtain a value of -0.67 ii) Sub known values into z = $\frac{x - \mu}{\sigma}$ and solve for $x$ -0.67 = $\frac{x - 69.4}{2.9}$ $x$ = $69.4$ + $(-0.67 \times 2.9)$ $x$ = 67.46 inches
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