Answer: 5.0%

The question involves calculating the probability that the returns on a combined fund will exceed a certain percentage, given that the returns on two independent funds are normally distributed. The Prudent Fund has a mean return of 3% and a standard deviation of 7%, while the Aggressive Fund has a mean return of 7% and a standard deviation of 15%. The combined fund is proposed to be a weighted sum of the two funds, with the weights determined by their asset sizes. The combined expected mean return (μ) is calculated by taking the weighted average of the individual means, which is \(0.2 \times 3\% + 0.8 \times 7\% = 6.2\%\). The combined volatility (standard deviation) is calculated using the formula for the standard deviation of a weighted sum of independent random variables: \[ \sigma = \sqrt{(0.2^2 \times 0.07^2) + (0.8^2 \times 0.15^2)} = 0.121 = 12.1\% \] The Z-statistic is then calculated to determine how many standard deviations the target return of 26% is away from the combined mean return: \[ Z = \frac{26\% - 6.2\%}{12.1\%} = 1.64 \] The probability that the returns on the combined fund will exceed 26% is equivalent to the probability that a standard normal variable is greater than 1.64. From the standard normal distribution table, the value \(P(Z > 1.64)\) is approximately 5%. Therefore, the correct answer is C. 5.0%. This is derived from the standard normal distribution, where the cumulative probability to the left of Z = 1.64 is 0.95, and thus the probability to the right is \(1 - 0.95 = 0.05\) or 5.0%.

Author: LeetQuiz Editorial Team