# 7.4 Summary of formulas

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Formula

## Central limit theorem for sample means

$\overline{X}$ ~ $N\left({\mu }_{X},\frac{{\sigma }_{X}}{\sqrt{n}}\right)\phantom{\rule{35pt}{0ex}}$ The Mean $\left(\overline{X}\right)$ : $\phantom{\rule{10pt}{0ex}}{\mu }_{X}$

Formula

## Central limit theorem for sample means z-score and standard error of the mean

$z=\frac{\overline{x}-{\mu }_{X}}{\left(\frac{{\sigma }_{X}}{\sqrt{n}}\right)}\phantom{\rule{25pt}{0ex}}$ Standard Error of the Mean (Standard Deviation $\left(\overline{X}\right)$ ): $\phantom{\rule{10pt}{0ex}}\frac{{\sigma }_{X}}{\sqrt{n}}$

Formula

## Central limit theorem for sums

$\mathrm{\Sigma X}$ ~ $N\left[\left(n\right)\cdot {\mu }_{X},\sqrt{n}\cdot {\sigma }_{X}\right]\phantom{\rule{10pt}{0ex}}$ Mean for Sums $\left(\mathrm{\Sigma X}\right)$ : $\phantom{\rule{10pt}{0ex}}n\cdot {\mu }_{X}$

Formula

## Central limit theorem for sums z-score and standard deviation for sums

$z=\frac{\mathrm{\Sigma x}-n\cdot {\mu }_{X}}{\sqrt{n}\cdot {\sigma }_{X}}\phantom{\rule{25pt}{0ex}}$ Standard Deviation for Sums $\left(\mathrm{\Sigma X}\right)$ : $\phantom{\rule{25pt}{0ex}}\sqrt{n}\cdot {\sigma }_{X}$