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.

Answer 1

Why are the calculations of a confidence interval still appropriate?

answer :

According to the central limit theorem any distribution is considered normal if n is greater than 30. 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.

According to CLT (central limit theorem) :

The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger. Sample sizes equal to or greater than 30 are considered sufficient for the CLT to hold.

Therefore as our n is 500 which is greater than 30, assuming normal distribution is appropriate,

thus, the calculations of a confidence interval still appropriate

P.S. (please upvote if you find the answer satisfactory)