5 The distribution of the sample means x can be approximated

5. The distribution of the sample means x can be approximated if: a) n = 20. The distribution is not Normal. b) n = 38. The distribution is not normal with Mux- = Mu and sigmax^- = sigma c) n = 16. The distribution is normal with Mux- = Mu and sigmax^- = sigma d) n = 25. The distribution is normal Mux-= Mu and sigmax^- = sigma/root n

Solution

a) n = 20, The distribution is not Normal.

Because according Central Limit Theorem, X_bar will have norma distribution for large sample sizes, generally for n> 30.

Thumb rule to follow is:

n > 30 : distribution of x_bar can be approximated as normal.