Homework SourseWhen estimating the mean of a probability distribution of so
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?
Solution
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.
