6.5 Summary of formulas

Central limit theorem for sample means

$\overline{X}$ ~ $\mathrm{N}({\mu }_X,\frac{{\sigma }_X}{\sqrt{n}})$ The Mean $\left(\overline{X}\right)$ : ${\mu }_X$

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

$z=\frac{\overline{x}-{\mu }_X}{\left(\frac{{\sigma }_X}{\sqrt{n}}\right)}$ Standard Error of the Mean (Standard Deviation $\left(\overline{X}\right)$ ): $\frac{{\sigma }_X}{\sqrt{n}}$

Central limit theorem for sums

$\mathrm{\Sigma X}$ ~ $N\left[\right(n)\cdot {\mu }_X,\sqrt{n}\cdot {\sigma }_X]$ Mean for Sums $\left(\mathrm{\Sigma X}\right)$ : $n\cdot {\mu }_X$

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

$z=\frac{\mathrm{\Sigma x}-n\cdot {\mu }_X}{\sqrt{n}\cdot {\sigma }_X}$ Standard Deviation for Sums $\left(\mathrm{\Sigma X}\right)$ : $\sqrt{n}\cdot {\sigma }_X$