Question

• Many times when you try to estimate a population mean, you do not know what the distribution is. The Central Limit Theorem allows any distribution to be turned into a) _____ distribution as long as n > 30. In this activity we turned an uniform distribution into this distribution using n=100. Even though the distribution changes, the b) ____ stays the same. However, the c) _______ becomes smaller. It is divided by .

Answer 1

Many times when you try to estimate a population mean, you do not know what the distribution is. The Central Limit Theorem allows any distribution to be turned into a) Normal distribution as long as n > 30. In this activity we turned an uniform distribution into this distribution using n=100. Even though the distribution changes, the b) mean stays the same. However, the c) variance becomes smaller. It is divided by .

a) Central limits theorem says that as n tends to infinity any distribution turns to normal distribution. But practically there is no need to goes for infinity for the value of n. We get result even n>30 easily.

b) In case of uniform distribution when n>50, the distribution changes to normal with same mean but c) reduced variance. The variance of the uniform distribution is already given by (b-a)^2/12. It becomes less as n gets large and large. Hence the answer.