\begin{equation}z_i=\frac{x_i-\overline{x}}{S_x}\end{equation} \begin{equation}\overline{z}=\sum\limits_{i=1}{n}\frac{x_i-\overline{x}}{S_x}=0 \end{equation} \begin{equation}S_z=1\end{equation}

$ $\begin{align} F(x) &= \frac 1{\sigma \cdot \sqrt{2\pi}} \cdot \int_{-\infty}^x \mathrm e^{-\frac 12 \cdot \left( \frac{t-\mu}{\sigma}\right)^2} \mathrm dt\ &= \frac 1{\sigma \cdot \sqrt{2\pi}} \cdot \int_{\frac{-\infty-\mu}\sigma}^{\frac{x-\mu}\sigma} \mathrm e^{-\frac 12 u^2} \mathrm du \cdot \sigma\ &= \frac 1{\sqrt{2\pi}} \cdot \int_{-\infty}^{\frac{x-\mu}\sigma} \mathrm e^{-\frac 12 u^2} \mathrm du\ &= \Phi \left(\frac{x-\mu}{\sigma}\right) \end{align}$ $

Statistik; Forschungsmethoden!Quantitative; Z-Transformation; ; ;

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