Elementary Statistics (12th Edition)

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

Chapter 5 - Discrete Probability Distributions - 5-2 Probability Distributions - Beyond the Basics - Page 210: 26


a)131,477.5 b)253,584.5 c)Minimum:-375691.5 Maximum:638646.5 d)They are unusually high.

Work Step by Step

a)There are 26 possibilites all with the same probability, hence the expected value is:$\frac{0.1}{26}+\frac{1}{26}+\frac{5}{26}+...+\frac{1,000,000}{26}=131,477.5.$ b)Standard deviation=$\sqrt{\frac{\sum (x-\mu)^2}{n}}=\sqrt{\frac{(0.1-131,477.5)^2+(1-131,477.5)^2+...+(1,000,000-131,477.5)^2}{26}}=253,584.5$ c) $Minimum \ usual \ value=mean-2\cdot(standard \ deviation)=131,477.5-2\cdot253,584.5=-375691.5$ $Maximum \ usual \ value=mean+2\cdot(standard \ deviation)=131,477.5+2\cdot253,584.5=638646.5$. d)Both of the values are more than 638646.5, hence they are both unusually high.
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