If a sample is normally distributed, is its population always normally distributed? I know this is correct: "If a population is normally distributed, a sample randomly chosen from it must be normally distributed." For instance, If the sizes of all apples of my farm are normally distributed, 50 apples chose from it should be normally distributed unless randomness was violated.
But, is the following as well correct? "If a sample randomly chosen from a certain population is normally distributed, the population must be normally distributed." That is, can I believe that its population is normally distributed, if I find a certain sample is normally distributed?

A sample only contains some information about the underlying distribution. And statistics gives you tools to check some properties of the underlying distribution. E.g., you can use hypothesis tests which tell you whether you can confidently reject the hypothesis that a sample originated from a normal distribution.
Thus, if tests like Shapiro-Wilk reject normality, you can be reasonably certain that the underlying distribution is not normal. If the test does not reject normality, you cannot really deduce anything.
