An assistant to the mayor, who claims to understand statistics, complains about

Question

An assistant to the mayor, who claims to understand statistics, complains about your confidence interval calculation. She asserts that the dollar losses from burglaries are not normally distributed, which in turn makes the confidence interval calculations meaningless. Assume that she is correct about the distribution of money loss. Why are the calculations of a confidence interval still appropriate? According to the central limit theorem any distribution is considered normal if n is greater than ____. This sample is 500 so the distribution of the sample means will be normal, no matter what the shape of the actual distribution of dollar losses.

Explanation / Answer

The central limit theorem applies to all distribution with sample size greater than 30 . As the sample size here is 500 > 30, therefore even if the distribution is not normal, with central limit theorem the process of confidence interval is valid.

Therefore 30 should be filled in the blank given.

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