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For questions about the central limit theorem, which states: "Given certain conditions, the mean of a sufficiently large number of iterates of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normally distributed." (Wikipedia)
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mean of population with repeated samples of varying size - how to apply CLT?
I have a population with mean $\mu$ and variance $\sigma^2$.
I draw a sample with $n_i$ number of i.i.d random observations from population. I compute the mean for this sample as $mean_i$. I then repe …