Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 7 - Section 7.2 - Assess Your Understanding - Explaining the Concepts - Page 380: 54

Answer

$P(Z \lt 30)$ should be considered as $\lt 0.0001$ Note that we should not round to "0", since this could give someone the impression that the event is not possible (i.e. will never occur).

Work Step by Step

First we need to calculate the z score: $z = \frac{x - μ}{σ} = \frac{30 - 100}{15} = -4.67$ $P(X \lt 30) = P(z \lt -4.67) = 1 - P(z \lt 4.67) = 1 - 0.9999 = 0.0001$ Hence, $P(Z \lt 30)$ should be considered as $\lt 0.0001$
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