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# Customers in a Bank A bank has a drive-through service. The number of customers arriving during a $15$-minute period is distributed as shown. Find the mean. variance, and standard deviation for the distribution.$\begin{array}{l|ccccc} \textbf{Number of customers} X & 0 & 1 & 2 & 3 & 4 \\ \hline \textbf{Probability} P(X) & 0.12 & 0.20 & 0.31 & 0.25 & 0.12 \end{array}$

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The mean $\mu$ of a random variable with a discrete probability distribution is the sum of the products of the outcomes $X$ and their corresponding probabilities $P(X)$.

$\mu=X_1\cdot P(X_1)\cdot X_2\cdot P(X_2)\cdot...\cdot X_n\cdot P(X_n)=\sum X\cdot P(X)$

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