Study on the Probability Distribution of Excellent Performance Rates

• 1、Department of Mathematics ang Applied Mathematics,Faculty of Science, Liaoning Technical University,FuXin 123100
• 2、

Abstract：The learning status of college students is often judged by their final grades, but considering that each major covers multiple disciplines, the complexity of conducting a detailed assessment for each subject is daunting. Therefore, this study takes students from a certain college as an example and uses the excellence rate of student grades to evaluate their learning performance. Firstly, the statistical patterns of the excellence rate data are revealed through expectation and variance analysis. Then, the distribution of the excellence rate is matched with the normal distribution density function by using the least squares fitting method, resulting in an approximate normal distribution density function. To further make the discrete excellence rate continuous and calculate the probability of corresponding intervals, a quadratic density function curve is constructed. By introducing the objective and constraint functions of the excellence rate model into the particle swarm optimization algorithm, the optimal quadratic density function is obtained after 1000 iterations. Finally, based on the optimal quadratic density function, the continuous distribution function of the excellence rate is derived, which can conveniently calculate the probability of any excellence rate interval, thereby providing a more accurate description of the students\' learning status. This model simplifies the process of grade evaluation and provides students with a more in-depth and comprehensive means of analyzing their learning status.

Keywords： Excellent erformance rate Probability distribution model Normal distribution Least squares fitting Tuna swarm optimization