This paper focuses on making normative methodology and interpretations for superior performing funds selection procedure on mean-variance efficient base. From the cross-sectional mutual fund return data analysis, the suggested superior performing funds are empirically from the best subset that contains all securities from the population with the largest normal mean and the smallest standard deviation of mutual fund return. Specifically, we concerned with this selection procedure under the combined mixtures of normal distribution hypothesis for fund returns without loosing the financial literature of the mutual fund business.