Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift.

$\begin{array}{|l|l|l|l|l|}
\hline \text {probability} & 0.10 & 0.25 & 0.55 & 0.10 \
\hline \text { \# of workers} & 3 & 4 & 5 & 6 \
\hline
\end{array}$

If the restaurant is open for 8 hours each day, what are the mean and standard deviation for the total number of workers in a day, respectively? (assume that the each hour is independent)
A) 37.2, 2.24
B) 37.2, 6.34
C) none of these
D) 36, 8.88
E) 36, 3.14

Question

Here is the distribution of workers a restaurant keeps on staff during a 1-hour shift.

$\begin{array}{|l|l|l|l|l|}
\hline   \text {probability} & 0.10 & 0.25 & 0.55 & 0.10 \
\hline  \text { \# of workers} & 3 & 4 & 5 & 6 \
\hline
\end{array}$

If the restaurant is open for 8 hours each day, what are the mean and standard deviation for the total number of workers in a day, respectively? (assume that the each hour is independent)
A) 37.2, 2.24
B) 37.2, 6.34
C) none of these
D) 36, 8.88
E) 36, 3.14

Quizplus · Accepted Answer

The mean number of workers per hour is $3(0.10) + 4(0.25) + 5(0.55) + 6(0.10) = 4.65$. For 8 hours, the mean is $8 \times 4.65 = 37.2$. The variance per hour is $(3-4.65)^2(0.10) + (4-4.65)^2(0.25) + (5-4.65)^2(0.55) + (6-4.65)^2(0.10) = 0.7$. For 8 hours, the variance is $8 \times 0.7 = 5.6$, so the standard deviation is $\sqrt{5.6} \approx 2.24$.

Here Is the Distribution of Workers a Restaurant Keeps on Staff