Formula Review

Central limit theorem for sample means: $\overline{X}$ ~ N$\left({\mu }_x\text{, }\frac{\sigma x}{\sqrt{n}}\right)$

Mean $\overline{X}$: μ_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 ($\overline{X}$)): $\frac{{\sigma }_x}{\sqrt{n}}$

Central limit theorem for sums: ∑X ~ N[(n)(μ_x),($\sqrt{n}$)(σ_x)]

Mean for sums (∑X): (n)(μ_x)

Central limit theorem for sums z-score and standard deviation for sums: $z\text{for the sample mean = }\frac{\Sigma x–(n)({\mu }_X)}{(\sqrt{n})({\sigma }_X)}$

Standard deviation for sums (∑X): $(\sqrt{n})$(σ_x)