Central Limit Theorem Applied to Predicting Underachievement among University Students

Purpose: The State Programme “Scientific and Technological Development of the Russian Federation” gives an important place to the training of a new generation of highly qualified engineers capable of ensuring the country’s technological sovereignty. Higher education institutions are being transformed into “advanced engineering schools” to train specialists in modern knowledge-intensive and multidisciplinary technologies. Greater attention is being paid to the disciplines of the first years of study, without which further study is incomplete. This article presents a method for predicting the number of underachieving students, which should help in planning measures to ensure timely implementation of the curriculum. Methods: The prediction of the number of underachieving students is based on the central limit theorem. The applicability of the central limit theorem is established using the Lyapunov condition. The convergence of the distribution of the number of underachieving students to Gauss’s law is studied using the Esseen inequality, while the empirical distribution function is modelled using the Monte Carlo method. Results: A confidence interval is constructed to estimate the number of underachieving students with known probabilities of underachievement for each student. A modification has been introduced to the reliability of the confidence interval for the deviation of the empirical distribution from Gauss Law. Practical significance: The interval prediction of the number of underachieving first-year students at the end of the academic year has been calculated.