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If samples of a population with size n are drawn, and the values of x-bar are calculated for each sample group, and the distribution of x-bar is found, the distribution’s shape is found to approach a normal distribution for sufficiently large n. This theorem allows one to use the assumption of a normal distribution when dealing with x-bar. “Sufficiently large” depends on the population’s distribution and what range of x-bar is being considered; for practical purposes, the easiest approach may be to take a number
of samples of a desired size and see if their means are normally distributed. If not, the sample size should be increased.