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 - Page 293: 7


a)0.0668 b)0.6985. c)The overhead reach distances are normally distributed and therefore the distribution of the sample mean is also normally distributed.

Work Step by Step

a) $z=\frac{value-mean}{standard \ deviation}=\frac{218.4-205.5}{8.6}=1.5$ Using the table, P(z>1.5)=1-P(z<1.5)=1-0.9332=0.0668. b) By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{204-205.5}{\frac{8.6}{\sqrt{9}}}=-0.52.$ Using the table, P(z>-0.52)=1-P(z)=1-0.3015=0.6985
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