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Problem 90: Voltage fluctuation is given as the reason for 80% of all defaults in nonstabilized equipment in a plant. Use the formula for the binomial distribution to find the probability that voltage fluctuation will be given as the reason for three of the next eight defaults.

Problem 90: Voltage fluctuation is given as the reason for 80% of all defaults in nonstabilized equipment in a plant. Use the formula for the binomial distribution to find the probability that voltage fluctuation will be given as the reason for three of the next eight defaults.

Solution:


Given that $x=3,n=8,$ and $p=0.8$
$P(x=3) = b(3;8,0.8)$
$b(x;n,p)=\left(\begin{array}{c}n\\ x\end{array}\right){p}^{x}(1-p)^{n-x}$
$P(x=3) = b(3;8,0.8) = \left(\begin{array}{c}8\\ 3\end{array}\right){0.8}^{3}(1-0.8)^{8-3} = 0.009175 $

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