117k views
0 votes
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?

User Toan Lu
by
8.0k points

1 Answer

3 votes

Answer:

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.

User Ralf Htp
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories