Question

Samples of weights of 200 students each are drawn from a normal population of the weights of students with S.D. 10

pound. Variance in each sample is computed. Find (i) mean (ii) standard deviation of the sampling distribution of sample

variance.

Answer 1

From the central limit theorem we see that the sampling distribution of the mean approaches a normal distribution with a mean of

$$E(\bar{X})=\mu_{\bar{X}}=\mu=50 \ kg$$

and a variance of

$${\sigma^2 \over n}={5^2 \over 30}={5 \over 6}$$

The standard deviation of the sampling distribution

$$\sigma_{\bar{X}}={5 \over \sqrt{30}}={\sqrt{30}\over 6}$$