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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.
Regression when the OLS residuals are not normally distributed. There are several threads on this site discussing how to determine if the OLS residuals are asymptotically normally distributed. Another way to evaluate the normality of the residuals with R code is provided in this excellent answer. This is another discussion on the practical difference between standardized and observed residuals. But let's say the residuals are definitely not normally distributed, like in this example.