Danke schon mal.
\documentclass{article}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=1.14}
% Gauss function, parameters mu and sigma
% #1 is \mu; #2 is \sigma
\pgfmathdeclarefunction{gaussian}{2}{ %exp(\frac{(x-\mu)^2}{2*\sigma^2})
\pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}} %\sigma*\sqrt{2*pi}
\begin{document}
\begin{center}
\begin{tikzpicture}
\begin{axis}[no markers, domain=97.8:102.2, samples=250, axis lines=left, xlabel=$x$, ylabel=$f_{X}(x)$,
every axis y label/.style={at=(current axis.above origin),anchor=south},
every axis x label/.style={at=(current axis.right of origin),anchor=west},
height=6cm, width=12cm, ymin=0, ymax=1.5,
ticks=none, %Ausblenden der Achsenskalierung, auskommentieren falls Skalen erwünscht
ytick={0.25,0.50,0.75,0.90,1},
xtick={97,97.5,98,98.5,99,99.5,100,100.5,101,101.5,102,102.5,103,103.5},
enlargelimits=false, clip=false, axis on top]
\addplot [very thick,cyan!50!black] {gaussian(100,0.8}; % #1 is \mu; #2 is \sigma^2
\addplot [very thick,cyan!50!black] {gaussian(100,0.5)};
\addplot [very thick,cyan!50!black] {gaussian(100,0.3)};
%\draw (axis cs: 100,-.1) node [fill=none] {$\mu$};
\draw [<-](axis cs: 100.30,1.1) -- (axis cs: 100.60,1.4) node [fill=white] {$\sigma_1$};
\draw [<-](axis cs: 100.65,0.5) -- (axis cs: 101.05,0.9) node [fill=white] {$\sigma_2$};
\draw [<-](axis cs: 101.25,0.2) -- (axis cs: 101.65,0.6) node [fill=white] {$\sigma_3$};
\draw (axis cs: 101.5,1.45) node [fill=none] {$\sigma_1<\,\sigma_2<\,\sigma_3$};
\draw [dotted](axis cs: 100,0) -- (axis cs: 100,1.3);
\end{axis}
\end{tikzpicture}
\end{center}
\end{document}
