Journal of Statistical Sciences, Autumn & Winter 2007 Vol. 1, No. 1   Inference in Normal Distribution Based on the Weighted Sampling   Alavi, S. M. R. and Chinipardaz, R.   Department of Statistics, Shahid Chamran University, Ahvaz, Iran.     Abstract:The classical analysis is based on random samples. However, in many situations the observations are recorded according to a nonnegative function of observations. In this case the mechanism of sampling is called weighted sampling. The usual statistical methods based on a weighted sample may be not valid and have to be adjusted. In this paper adjusted methods under some particular weight functions for normal distribution are studied and a new distribution called double normal distribution, is introduced as a weighted normal distribution.   Keywords:Weighted Sampling, Independent Weight Function, Dependent Weight Function, Weighted Random Variable, Weighted Normal Distribution, Double Normal Distribution.