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

No.

Explanation:

According to the central limit theorem,

• if the samples are large (greater than​30)
• sampling is random

Then the distribution of sample means can be approximated by a normal distribution. And the mean of this distribution converges true mean of annual incomes.

But distribution of annual incomes inside a sample may not be normal.