In the theory of fuzzy measures, Choquet integral is one of the most important tools. The calculation of Choquet integral on real line is difficult for many cases such as nonmonotone functions. In this paper, by the geometric interpretation of Choquet integral, we introduce a new Choquet-like integral with a different algebraic interpretation of Choquet integral on real line. The calculation of this integral is simpler than Choquet integral on real line. Based on this integral, we introduce a general class of normal distribution on monotone measures. Finally, as an application, the real dataset obtained from the daily price of Dow Jones Industrial Average Index in period of June 2, 2008 to June 2, 2018 is analyzed.