Answer: 99.38% for Fund X.

## Explanation To find the probability of earning a return in excess of 20% for each mutual fund, we need to calculate the z-score for each fund and use the z-table to find the corresponding probability. ### Z-Score Formula: \[ Z = \frac{\text{Desired Return} - \text{Mean Return}}{\text{Standard Deviation}} \] ### Calculations: **Fund X:** - Mean = 25%, Std. Dev. = 2% - \[ Z = \frac{20\% - 25\%}{2\%} = \frac{-5\%}{2\%} = -2.5 \] - P(Z < -2.5) ≈ 0.0062 (from z-table) - P(X > 20%) = 1 - P(Z < -2.5) = 1 - 0.0062 = 0.9938 = **99.38%** **Fund Y:** - Mean = 24.8%, Std. Dev. = 3% - \[ Z = \frac{20\% - 24.8\%}{3\%} = \frac{-4.8\%}{3\%} = -1.6 \] - P(Z < -1.6) ≈ 0.0548 (from z-table) - P(Y > 20%) = 1 - P(Z < -1.6) = 1 - 0.0548 = 0.9452 = **94.52%** **Fund Z:** - Mean = 26%, Std. Dev. = 4% - \[ Z = \frac{20\% - 26\%}{4\%} = \frac{-6\%}{4\%} = -1.5 \] - P(Z < -1.5) ≈ 0.0668 (from z-table) - P(Z > 20%) = 1 - P(Z < -1.5) = 1 - 0.0668 = 0.9332 = **93.32%** ### Analysis of Options: - **Option A (1.60% for Fund Y)** - Incorrect, this is approximately P(Z < -1.6) not P(Y > 20%) - **Option B (94.52% for Fund Z)** - Incorrect, this is actually the probability for Fund Y - **Option C (99.38% for Fund X)** - **CORRECT** - Matches our calculation for Fund X - **Option D (11.6% for Fund Y)** - Incorrect, this doesn't match any of our calculated probabilities Therefore, the correct answer is **C** - 99.38% for Fund X.

Author: Tanishq Prabhu