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.
Central limit theorem states that as a sample being studied grows larger the sampling distribution of samplings means tends to a more normal distribution. This is regardless of the shape of the population.
This holds true usually if the population size is n is equal or greater than 30 (that is greater than 29). It does not matter if the population is skewed or normal.
So with a sufficiently large population the means of each item will be the same as the population mean.
Explanation is in a file
about your confidenc...