Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 6 - Normal Probability Distributions - 6-5 The Central Limit Theorem - Basic Skills and Concepts: 3

Answer

$mean=\mu_{\overline{x}}=60.5 cm$ $standard \ deviation=\sigma_{\overline{x}}=1.1cm$

Work Step by Step

The size of the sample(36) is 30 or more, therefore by the Central Limit Theorem the distribution of the mean ages is basically a normal distribution. Hence, $mean=\mu_{\overline{x}}=\mu=60.5 cm$ $standard \ deviation=\sigma_{\overline{x}}=\frac{\sigma}{\sqrt n}=\frac{6.6cm}{\sqrt{36}}=\frac{6.6cm}{6}=1.1cm$
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