Answer: 5.0%

The question pertains to the probability of the combined returns of two funds exceeding a certain threshold. The Prudent Fund and the Aggressive Fund have different means and standard deviations for their returns, which are normally distributed and independent of each other. To find the combined expected mean return and volatility, we use the weighted averages of their respective means and variances, considering the proportion of each fund's assets in the combined fund. The combined expected mean return (μ) is calculated as follows: \[ \mu = 0.2 \times 3\% + 0.8 \times 7\% = 6.2\% \] The combined volatility (σ) is calculated by taking the square root of the weighted sum of the variances: \[ \sigma = \sqrt{0.2^2 \times 0.07^2 + 0.8^2 \times 0.15^2} = 0.121 = 12.1\% \] The Z-statistic is then used to determine the probability that the returns on the combined fund will exceed 26%. The Z-statistic is calculated by subtracting the combined mean return from 26% and dividing by the combined volatility: \[ Z = \frac{26\% - 6.2\%}{12.1\%} = 1.64 \] Using the standard normal distribution table or a calculator, we find that the probability of a Z-score being greater than 1.64 is 0.05, which corresponds to 5.0%. Therefore, the probability that the returns on the combined fund will exceed 26% is 5.0%, making option C the correct answer. This question tests the understanding of the properties of normally distributed random variables and the calculation of the mean and variance of a weighted sum of independent random variables.

Author: LeetQuiz Editorial Team