A firm making production plans believes there is a 30% probability the price will be $10,a 50% probability the price will be $15,and a 20% probability the price will be $20.The manager must decide whether to produce 6,000 units of output (A),8,000 units (B)or 10,000 units (C).The following table shows 9 possible outcomes depending on the output chosen and the actual price. $$\begin{array} { c c c c }
&{ \text { Prand (Lasi) when price is } } \
\text { Pradiction } & \$ 10 & \$ 15 & \$ 20 \
\hline 6,000 ( A ) & - \$ 200 & \$ 400 & \$ 1,000 \
\text { B,000 } ( B ) & - \$ 400 & \$ 600 & \$ 1,600 \
10,000 ( C ) & - \$ 1,000 & \$ 800 & \$ 3,000
\end{array}$$ What is the variance if 6,000 units are produced?
A)490,000
B)176,400
C)100,000
D)68,200
E)76,460

Question

A firm making production plans believes there is a 30% probability the price will be $10,a 50% probability the price will be $15,and a 20% probability the price will be $20.The manager must decide whether to produce 6,000 units of output (A),8,000 units (B)or 10,000 units (C).The following table shows 9 possible outcomes depending on the output chosen and the actual price. $$\begin{array} { c c c c } 
&{ \text { Prand (Lasi) when price is } } \
 \text { Pradiction } & \$ 10 & \$ 15 & \$ 20 \
\hline 6,000 ( A ) & - \$ 200 & \$ 400 & \$ 1,000 \
\text { B,000 } ( B ) & - \$ 400 & \$ 600 & \$ 1,600 \
10,000 ( C ) & - \$ 1,000 & \$ 800 & \$ 3,000
\end{array}$$ What is the variance if 6,000 units are produced?
A)490,000
B)176,400
C)100,000
D)68,200
E)76,460

Quizplus · Accepted Answer

The variance is calculated by finding the expected value of the squared deviations from the mean. First, calculate the expected profit: $0.3 \times (-200) + 0.5 \times 400 + 0.2 \times 1000 = 340$. Then, calculate the squared deviations: $((-200) - 340)^2 \times 0.3 + (400 - 340)^2 \times 0.5 + (1000 - 340)^2 \times 0.2 = 176,400$.

A Firm Making Production Plans Believes There Is a 30