When estimating the mean of a probability distribution of some population of Int

Question

When estimating the mean of a probability distribution of some population of Interest( variance known), a confidence interval is typically constructed using a normal distribution, even if the underlying population distribution is not normal. Why is this done? When estimating the mean of a probability distribution of some population of Interest( variance known), a confidence interval is typically constructed using a normal distribution, even if the underlying population distribution is not normal. Why is this done?

Explanation / Answer

whenever a confidence interval is constructed ,it is based on a sample. let the sample size be n

now from CENTRAL LIMIT THEOREM as n tensed to infinity the underlined population distribution can be approximated by a normal distribution.

and in real life situations n is taken sufficiently large so that this approximation can be valid.

hence the confidence interval is typically constructed using a normal distribution.

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