Question

7. 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 (n>30) random sample of annual incomes.

a. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is large? Why or why not?

b. What is the approximate shape of the distribution of the sample means (Uniform, normal, skewed, other?)

c. What value do the sample means target? That is, what is the mean of all such sample means?

Answer 1

a. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is large? Why or why not?

Yes, the distribution of incomes in that sample can be approximated by a normal distribution by central limit theorem, since n>30.

b. What is the approximate shape of the distribution of the sample means (Uniform, normal, skewed, other?)

Ans : NORMAL

c. What value do the sample means target? That is, what is the mean of all such sample means?

Ans : Population mean