## Related questions with answers

The following table, reproduced from earlier exercise, gives the probability distribution of the number of patients who enter Millard Fellmore Memorial Hospital's emergency room in a given hour.

$\begin{array}{l|ccccccc} \hline \text { Patients per hour } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Probability } & .2725 & .3543 & .2303 & .0998 & .0324 & .0084 & .0023 \\ \hline \end{array}$

Calculate this probability distribution's mean and standard deviation.

Solution

VerifiedRecall the formulas for the mean, $\mu$, and the standard deviation, $\sigma$:

$\begin{aligned} \mu&=\sum xP(x)\\ \sigma&=\sqrt{\sum x^2P(x)-\mu^2} \end{aligned}$

For this problem, $x$ refers to the number of patients entering the emergency room during a $1$-hour period at Millard Fellmore Memorial Hospital

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