Central Limit Theorem

${\bar{x}}_n\sim N({\mu }_{\bar{x}},{\sigma }_{\bar{x}})$ ${\bar{x}}_n\sim N(\mu ,\frac{\sigma }{\sqrt{n}})$

• when $n$ is large enough (large sample size) then we can assume the sample mean $\bar{x}$ to be equivalent to population mean $\mu$
  • it is not equivalent, but close enough realistically
• then the standard deviation
• basically we can use $s$ for $\sigma$
  • $\sigma$ is rarely known, so we need to work around that