Answer: [-0.4%; 3.4%]

## Explanation To calculate the 99% confidence interval for the quarterly returns, we use the formula: **Standard error of the sample mean** = $\frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}}$ Given: - Sample size (n) = 121 - Standard deviation (σ) = 8% = 0.08 - Sample mean (x̄) = 1.5% = 0.015 - 99% confidence level **Step 1: Calculate standard error** $$SE = \frac{0.08}{\sqrt{121}} = \frac{0.08}{11} = 0.00727$$ **Step 2: Find critical z-value** For 99% confidence interval, the critical z-value is 2.575 **Step 3: Calculate margin of error** $$Margin\ of\ error = z \times SE = 2.575 \times 0.00727 = 0.0187$$ **Step 4: Calculate confidence interval** $$CI = x̄ \pm margin\ of\ error = 0.015 \pm 0.0187$$ $$Lower\ bound = 0.015 - 0.0187 = -0.0037 = -0.37\%$$ $$Upper\ bound = 0.015 + 0.0187 = 0.0337 = 3.37\%$$ Therefore, the 99% confidence interval is approximately **[-0.37%; 3.37%]**, which matches option A [-0.4%; 3.4%].

Author: Tanishq Prabhu