Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2008.1122.1124BevraniH.GhorbaniM.SadaghianiM.K.6200886In this study, we construct the optimal estimator for sample size, which were sufficient for maintenance the demanded accuracy and reliability. The goal of this paper is presenting three estimators such as follow. The first one which is traditional approach and rough enough is based on the Chebyshev`s inequality. The second one is based on the central limit theorem, but it doesn`t take into account the accuracy of the normal approximation. The third estimator is based on Berry-Esseen`s inequality that takes into account the accuracy of the normal approximation and is guaranteed.]]>Bauer, W.F.,1958Bevrani, H.,2003Ermakov, S.M.,1971Gentle, J.E.,2004Korolev, V.Y. and I.G. Shevtsova,2006Rubinstein, R.Y.,1981Shiganov, I.S.,1986