Let's break down the steps to calculate the standard deviation for each of the expansion plans, assuming we have the probability distribution for the increased demand of flip-flops.

Step 1: Review Expected Value Formula

The expected value (mean) $E(x)$ is given by:

$E(x) = \sum (x_i \cdot p_i)$

Where:

• $x_i$ is the profit for a particular demand level.
• $p_i$ is the probability of that particular demand.

Step 2: Standard Deviation Formula

The formula for standard deviation $\sigma_x$ is:

$\sigma_x = \sqrt{\sum \left( (x_i - E(x))^2 \cdot p_i \right)}$

Where:

• $E(x)$ is the expected value (profit), which has already been computed for each plan.
• $x_i$ represents the profit values for different demand levels.
• $p_i$ is the corresponding probability of each demand level.

To calculate the standard deviation for each expansion plan, we need:

1. The demand levels and their probabilities.
2. The formula to calculate the variance by plugging in the expected value $E(x)$, the profit values $x_i$, and the probabilities $p_i$.

Please share the probability distribution of the increased demand, and I will help you compute the standard deviation.

Would you like a detailed step-by-step explanation on how to compute the standard deviation for each plan?

Five Related Questions:

1. How is the expected profit for each plan affected by changes in demand probability?
2. How would changing the cost structure (e.g., increasing the yearly costs) impact the expected profit and risk?
3. What happens to the standard deviation if the probabilities of lower demand increase?
4. How can we interpret the standard deviation in terms of business risk?
5. What other factors (like market conditions) might affect the choice of expansion plan?

Tip:

Always consider both expected profit and standard deviation when making business decisions to balance potential profit with associated risk.