Moderate# Understanding Central Limit Theorem

STATS-9JLAXG

Let $\bar{X}$ be the experiment of collecting a sample of size 50 from a population with mean $\mu=10$ and variance $\sigma^2=16$.

Consider the following four statements below:

i.The random variable defined by $\dfrac{\bar{X}-10}{\dfrac{4}{\sqrt{50}}}$ is a Standard Normal random Variable.

ii.The variance of $\dfrac{\bar{X}-10}{4}$ is 1.

iii.The probability that the outcome of $\bar{X}$ is smaller than 10 is .5.

iv.The probability that the outcome of $\dfrac{\bar{X}-10}{\dfrac{4}{\sqrt{50}}}$ is smaller than 0 is .5.