How many measurements must you have in order to be sure the sampling distribution of x¯ is normal?
Update:
Suppose you are dog breeder and you want to use a confidence interval to estimate the true mean fertility levels of purebred cocker spaniels. It is known that the distribution of fertility levels of cocker spaniels is normal. How many measurements must you have in order to be sure the sampling distribution of x¯ is normal?
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If the underlying distribution is normal, one. Otherwise a sufficient number approximates a normal.
For example, the sum of 3 uniform random variables is already a fair approximation to a normal except for lightness in the tails.