Question: How large a sample size is needed to estimate the mean annual income of natives of Country X correct to within $1,000 with probability 0.99?

How large a sample size is needed to estimate the mean annual income of natives of Country X correct to within $1,000 with probability 0.99? There is no prior information about the standard deviation of annual income of natives, but we guess that about 95% of their incomes are between $6,000 and $66,000 and that this distribution of incomes is skewed but approximately bell shaped.

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