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 workers are paid $10/hour, what is the expected long-term cost of a 1-hour shift?
A) none of these
B) $180
C) $46.50
D) $4.65
E) $45

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 workers are paid $10/hour, what is the expected long-term cost of a 1-hour shift?
A) none of these
B) $180
C) $46.50
D) $4.65
E) $45

Quizplus · Accepted Answer

To find the expected long-term cost, we must multiply the number of workers in each category by their respective hourly wage and then sum those products.

Category 1: 4 workers x $10/hour = $40/hour
Category 2: 10 workers x $10/hour = $100/hour
Category 3: 6 workers x $10/hour = $60/hour

Total cost = $40 + $100 + $60 = $200

However, we are looking for the expected long-term cost, which means we need to account for the probability of each category occurring during a shift.

Category 1 occurs with probability 0.1, category 2 occurs with probability 0.7, and category 3 occurs with probability 0.2.

Expected cost = (0.1 x $40) + (0.7 x $100) + (0.2 x $60) = $46.

Therefore, the expected long-term cost of a 1-hour shift is $46.50. Answer choice C is correct.

Here Is the Distribution of Workers a Restaurant Keeps on Staff