Answer: 5.0%

## Explanation Since the returns on the two funds are independent and normally distributed, we can calculate the combined expected return and volatility using portfolio theory. **Step 1: Calculate portfolio weights** - Prudent Fund: USD 50 million - Aggressive Fund: USD 200 million - Total assets: USD 250 million - Weight of Prudent Fund: 50/250 = 0.2 (20%) - Weight of Aggressive Fund: 200/250 = 0.8 (80%) **Step 2: Calculate combined expected return** $$ \mu = w_1 \cdot \mu_1 + w_2 \cdot \mu_2 = 0.2 \cdot 3\% + 0.8 \cdot 7\% = 0.6\% + 5.6\% = 6.2\% $$ **Step 3: Calculate combined volatility** Since the returns are independent (correlation = 0): $$ \sigma = \sqrt{w_1^2 \cdot \sigma_1^2 + w_2^2 \cdot \sigma_2^2} = \sqrt{0.2^2 \cdot 0.07^2 + 0.8^2 \cdot 0.15^2} $$ $$ \sigma = \sqrt{0.04 \cdot 0.0049 + 0.64 \cdot 0.0225} = \sqrt{0.000196 + 0.0144} = \sqrt{0.014596} = 0.121 = 12.1\% $$ **Step 4: Calculate Z-statistic for 26% return** $$ Z = \frac{X - \mu}{\sigma} = \frac{26\% - 6.2\%}{12.1\%} = \frac{19.8\%}{12.1\%} = 1.64 $$ **Step 5: Find probability** We want P(Z > 1.64) = 1 - P(Z ≤ 1.64) = 1 - 0.95 = 0.05 = 5.0% Therefore, the probability that the returns on the combined fund will exceed 26% is 5.0%.

Author: LeetQuiz .