The normal distribution plays an important role in constructing interval statistical estimates of the numerical characteristics of random processes. In most cases, under the same conditions, the sum of random variables that do not differ significantly from each other will have a normal distribution based on the central limit theorem of probability theory. In this research, the authors analyzed the average annual number of passengers transported by the railway transport company in the Republic of Uzbekistan. The primary statistical hypothesis assumes a normal distribution. The alternative hypothesis, based on the Shapiro-Wilcoxon test, suggests that the data do not follow a normal distribution. To validate these hypotheses, the authors used Pearson and parametric tests. The authors also calculated the key numerical characteristics of the average annual passenger numbers in the Republic of Uzbekistan. The results of this analysis help reduce uncertainty, enhance the accuracy of passenger flow forecasting, and improve the planning and management practices of the railway transport company in the Republic of Uzbekistan.