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Expert-verified Found in: Page 205 ### Statistics For Business And Economics

Book edition 13th
Author(s) James T. McClave, P. George Benson, Terry Sincich
Pages 888 pages
ISBN 9780134506593 # Monitoring quality of power equipment. Mechanical Engineering (February 2005) reported on the need for wireless networks to monitor the quality of industrial equipment. For example, consider Eaton Corp., a company that develops distribution products. Eaton estimates that 90% of the electrical switching devices it sells can monitor the quality of the power running through the device. Eaton further estimates that of the buyers of electrical switching devices capable of monitoring quality, 90% do not wire the equipment up for that purpose. Use this information to estimate the probability that an Eaton electrical switching device is capable of monitoring power quality and is wired up for that purpose.

The probability that an Eaton electrical switching device is capable of monitoring power quality and is wired up for that purpose is 0.09.

See the step by step solution

## Important formula

The formula for probability is $\mathbf{P}\mathbf{\left(}{{\mathbf{A}}}^{c}\mathbf{\right)}\mathbf{=}\mathbf{1}\mathbf{-}\mathbf{P}\mathbf{\left(}\mathbf{A}\mathbf{\right)}$.

## The probability that an Eaton electrical switching device is capable of monitoring power quality and is wiredup for that purpose.

Here, $\mathrm{P}\left(\mathrm{A}\right)=90\mathrm{%}=0.9$

$\mathrm{P}\left(\mathrm{B}|\mathrm{A}\right)=90\mathrm{%}=0.9$

Now, find the result, then,

$\begin{array}{c}\mathrm{P}\left({\mathrm{B}}^{\mathrm{C}}|\mathrm{A}\right)=1-\mathrm{P}\left({\mathrm{B}}^{\mathrm{C}}|\mathrm{A}\right)\\ =1-0.9\\ =0.1\\ \mathrm{P}\left(\mathrm{A}\cap {\mathrm{B}}^{\mathrm{C}}\right)=\mathrm{P}\left({\mathrm{B}}^{\mathrm{C}}|\mathrm{A}\right)\mathrm{P}\left(\mathrm{A}\right)\\ =\left(0.1\right)\left(0.9\right)\\ =0.09\end{array}$

Therefore, the probability is 0.09.

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