SpringerIranian Journal of Science and Technology (Sciences)1028-627632120080217ON THE DISTRIBUTION OF Z-SCORES7178224510.22099/ijsts.2008.2245ENJ.BEHBOODIANDepartment of Mathematics, Islamic Azad University, Shiraz, I. R. of IranA.ASGHARZADEHDepartment of Statistics, Faculty of Basic Sciences, Mazandaran University, Babolsar, I. R. of IranJournal Article20061028Let X ,..., Xn 1 be a random sample from a distribution with sample mean X and sample<br />variance S 2. In this paper we consider certain very general properties of the so-called “Z-scores”<br />X X S i n i ( − )/ : = 1,...., . A representation theorem is then given for Z-scores obtained from an underlying<br />normal population, together with a theorem for their limiting distribution as the sample size tends to infinity.<br />Finally, two applications involving grading and testing for an outlier are presented.http://ijsts.shirazu.ac.ir/article_2245_7c4086e2bf5cb1aaec28c2c0824b1b6e.pdf