Essentials of Statistics (5th Edition)

Published by Pearson
ISBN 10: 0-32192-459-2
ISBN 13: 978-0-32192-459-9

Chapter 5 - Discrete Probability Distributions - 5-4 Parameters for Binomial Distributions - Page 228: 20


a) Mean:0.000013. Standard deviation:0.003649. b)It is unusual.

Work Step by Step

Here, n=$2600, p=\frac{1}{195249054}.$ a) Mean=$n\cdot p=2600 \cdot \frac{1}{195249054}=0.000013$. Standard deviation: $\sqrt{n \cdot p \cdot (1-p)}=\sqrt{2600 \cdot \frac{1}{195249054} \cdot \frac{195249053}{195249054}}=0.003649.$ b) If a value is unusual, then it is more than two standard deviations far from the mean. $Minimum \ usual \ value=mean-2\cdot(standard \ deviation)=0.000013-2\cdot0.003649=-0.007285$ $Maximum \ usual \ value=mean+2\cdot(standard \ deviation)=0.000013+2\cdot0.003649=0.007311$. 1 is more than the upper bound (and the lower bound), therefore it is unusual.
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