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 292: 5


a) 0.9772. b)0.8888.

Work Step by Step

a) $z=\frac{value-mean}{standard \ deviation}=\frac{222.7-205.5}{8.6}=2.$ Using the table, the value belonging to 2: 0.9772. b) By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{207-205.5}{\frac{8.6}{\sqrt{49}}}=1.22.$ Using the table, the value belonging to scores less than 1.22: 0.8888.
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