Question

Data will be drawn independently from a normal distribution N(5, 4), i.e. with mean 5 and variance 4. A single observation will be termed X. The sample mean (average) of n observations will be termed X. If the sample size drawn is n = 100, derive the distribution of X.

Answer 1

Solution :

If X is a population which is normally distributed with mean μ and variance then, sampling distribution of sample mean (x̄) follows normal distribution with mean μ and variance . (Where, n is sample size.)

We have, X ~ N(5, 4)

i.e.   and   

Sample size (n) = 100

Hence, the distribution of x̄ will be normal with mean 5 and variance 0.04.

Symbolically,  .