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 2 - Describing Distributions with Numbers - Check Your Skills: 2.22

Answer

a) $0 \leq x$

Work Step by Step

A standard deviation is the square root of the sum of the variances. Since the sum of the variances is (almost) always greater than 1--and never negative--the standard deviation would be greater than 1 (except for when the sum of the variances is smaller than 1, when the standard deviation would also be less than 1).
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