Question: If we wish to model our sample means (-bar) with a Normal distribution, then our samples should have a certain minimum sample size and that

If we wish to model our sample means (-bar) with a Normal distribution, then our samples should have a certain minimum sample size and that minimum would depend on the shape of the original parent population. But what if we have a sample and we don't know the shape of the population that it came from. What shape should the population have had, if we want to use a Normal model for X-bar? Match the sample sizes given below with the worst-case shape requirement. For example, if our sample size is 9, then our population would need to have been at worst bell-shaped. As in, it is okay for it to be Normal or bell-shaped-but-not-Normal, but it is not okay for it be symmetric-but-not-bell-shaped and it absolutely may not be skewed.

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