Question

Given a population with mu = 64 and sigma = 25, if one draws samples of size l55, the sample means will have a distribution which is approximately normal with:

Answer 1

Solution: We are given a population follows a normal distribution with Mean $\mu=64$ and standard deviation $\sigma=25$

According to central limit theorem, if we have a population with mean $\mu$ and standard deviation $\sigma$ and take large samples from the population, then the distribution of samples means will be approximately normally distributed with mean and standard deviation given below:

$\mu_{\bar{x}}=\mu$

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$

Therefore, for the given example the distribution of sample means will be approximately normal with mean and standard deviation given below:

$\mu_{\bar{x}}=\mu=64$

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{25}{\sqrt{155}}=2.01$ rounded to 2 decimal places.