Interpret the Mean of a Discrete Random Variable as an Expected Value
-A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below:
$\begin{array}{l|ccc}
\text { Price } & \$ 10.00 & \$ 12.50 & \$ 15.00 \
\hline \text { Probability } & 0.2 & 0.3 & 0.5
\end{array}$

How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint: find the expected price.)
A) $\$ 689.00$
B) $\$ 13.25$
C) $\$ 1325.00$
D) $\$ 3,582,800.00$

Question

Interpret the Mean of a Discrete Random Variable as an Expected Value
-A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below:
$\begin{array}{l|ccc}
\text { Price } & \$ 10.00 & \$ 12.50 & \$ 15.00 \
\hline \text { Probability } & 0.2 & 0.3 & 0.5
\end{array}$

How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint: find the expected price.)
A) $\$ 689.00$
B) $\$ 13.25$
C) $\$ 1325.00$
D) $\$ 3,582,800.00$

Quizplus · Accepted Answer

The expected price is the mean of the distribution, which is:$$E(X) = 10(0.2) + 12.5(0.3) + 15(0.5) = 13.25$$So the lab should budget for $13.25 per week, or $13.25 * 52 = $689.00 for the year.