An Introduction to Mathematical Statistics and Its Applications (6th Edition)

Published by Pearson
ISBN 10: 0-13411-421-3
ISBN 13: 978-0-13411-421-7

Chapter 3 Random Variables - 3.5 Expected Values - Questions - Page 153: 29

Answer

$\color{blue}{\$132}$

Work Step by Step

Let $Y$ be the random variable denoting the number of defective components among the 12 electronic components produced daily. Then $Y$ has a binomial distribution with $n=12$ and $p=0.11$ so that by Theorem 3.5.1 (see p. 139-40), $\begin{align*} E(Y)& =np \\ &= 12(0.11) \\ E(Y) &= 1.32 \end{align*}$ Thus, the expected number of defective components among the 12 components produced daily is 1.32. Since reworking a component that is defective costs \$100, then the average daily costs for defective components is given by $\color{blue}{E(Y)\cdot $100 =1.32(\$100) = \$132.}$
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