Answer: 0.62% for Fund X

The correct answer is C) 0.62% for Fund X. **Step-by-step explanation:** 1. **Calculate z-values for each fund:** - Fund X: z = (20% - 15%) / 2% = 5% / 2% = 2.5 - Fund Y: z = (20% - 15.20%) / 3% = 4.8% / 3% = 1.60 - Fund Z: z = (20% - 14%) / 4% = 6% / 4% = 1.50 2. **Use z-table to find cumulative probabilities:** - For z = 2.5: Cumulative probability = 99.38% (probability of return ≤ 20%) - For z = 1.60: Cumulative probability = 94.52% - For z = 1.50: Cumulative probability = 93.32% 3. **Calculate probability of return > 20%:** - Fund X: 100% - 99.38% = 0.62% - Fund Y: 100% - 94.52% = 5.48% - Fund Z: 100% - 93.32% = 6.68% 4. **Compare with given options:** - Option A (1.60% for Fund Y) is incorrect - actual probability is 5.48% - Option B (5.78% for Fund Z) is incorrect - actual probability is 6.68% - Option C (0.62% for Fund X) is correct - Option D (11.6% for Fund Y) is incorrect **Key concept:** When returns are normally distributed, the z-score measures how many standard deviations a value is from the mean. The z-table gives the cumulative probability from negative infinity to that z-value. To find the probability of exceeding a value, subtract the cumulative probability from 100%.

Author: Nikitesh Somanthe