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Thus based on the data in the sample an sich (as calculated by a test for normality), it is unlikely that the sample is part of a normal distribution, but we already know it is part of a normal distribution, because it's part of population that is normally distributed.
The population distribution just has to have finite first and second moments, so that Ï 2 is actually defined. On the other hand, the following results relating to unbiased estimation of Ï itself require that we are sampling from a normal population.