Question

Annual incomes are known to have a distribution that is skewed to the right instead of being normally distributed. Assume that we collect a large ?(ngreater than?30) random sample of annual incomes. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is? large? Why or why? not?

Answer 1

Central Limit Theorem states that for a population with any distribution, the distribution of sample mean approaches Normal distribution as the sample size increases.

Note: For following CLT, Original population must have n>30.Here ,population distribution is skewed. If we want to find sampling distribution of mean income in sample, then only here CLT can be used for Normal approximation in sample mean beacuse the sample n is greater than 30 ,but otherwise not.