Question

1.) if samples of very small size, n, (say n=2) are drawn from a normally distributed population, the distribution of the sample means is distributed as?

a) skewed distribution

b) not any particular distribution we have studied, but not skewed

c) binomial distribution

d) normal distribution

----

2) if samples of very small size, n, (say n=2) are drawn from a uniformly distributed population, the distribution of the sample means is distributed as?

a) skewed distribution

b) not any particular distribution we have studied, but not skewed

c) binomial distribution

d) normal distribution

Answer 1

1.) if samples of very small size, n, (say n=2) are drawn from a normally distributed population, the distribution of the sample means is distributed as?

Answer - d) normal distribution

2) if samples of very small size, n, (say n=2) are drawn from a uniformly distributed population, the distribution of the sample means is distributed as?

Answer - d) normal distribution

Central limit theorem tells that if we have large number of independent and identically distributed variables the distribution will approximately follow the normal distribution.

Here large means sample size (n) should be greater than 30.

But this have some exception

We have small sample size but Samples are drawn from Normal and Uniform Distribution.

If we draw the sample from Normal and Uniform multiple times and plot there sample means we can find that this follow Normal distribution.