ab582cf4-dabd-41f9-86e2-a2afb3466edd20230712050755750wseas:wseasmdt@crossref.orgMDT DepositEQUATIONS2732-99762944-914610.37394/232021https://wseas.com/journals/equations/41220234122023310.37394/232021.2023.3https://wseas.com/journals/equations/2023.phpHassanHajiDepartment of Statistics Imam Khomeini International University Qazvin, IRANIn this paper, we derive an upper bound on the Kolmogorov distance between the distribution of a sum of indicator random variables and a standard normal distribution by using the size-bias method. Also, we give lower and upper bounds for distribution function of sum of indicator random variables in two special points.7122023712202325283https://wseas.com/journals/equations/2023/a065106-1739.pdf10.37394/232021.2023.3.3https://wseas.com/journals/equations/2023/a065106-1739.pdfArratia, R. Goldstein, L., Size bias, sampling, the waiting time paradox, and infinite divisibility: when is the increment independent, Available in http://bcf.usc.edu/ larry/papers/pdf/csb.pdf, . 2009. Arratia, A. Goldstein, L. and Kochman, F., Size-bias for one and all, Preprint. Available at arXiv: 1308.2729, 2013. Billingsley, P., Probability and Measure, John Wiley and Sons, New York, 1885. 10.1007/s00440-009-0253-3Ghosh, S. and Goldstein, L., Concentration of measures via size-biased couplings. Porbability Theory and Related Fields, 2011, 149, 271-278. 10.1214/ecp.v16-1605Ghosh, S. and Goldstein, L., Applications of size biased couplings for concentration of measures, Electronic Communications in Probability, 2011, 16, 70-83. 10.2307/3215259Goldstein, L. and Rinott, Y., Multivariate normal approximations by Stein’s method and size bias couplings, Journal of Applied Probability, 1996, 33(1), 1-17. Ross, N., Fundamentals of Stein’s method, Probability Surveys, 2011, 8, 210-293.