Bell curve with multiple x-axes and annotations

Question

I've just started working with pgfplots and I'm getting good results, but I'm having difficulties getting this one done in LaTeX:

The curve itself is not a problem, but the multiple x-axes (I don't need the top one, just the middle and the bottom ones) and especially the "68.2%" right in the middle of the plot just won't work.

Here's what I got so far:

    \pgfmathdeclarefunction{gauss}{2}{%
    \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
        }

    \begin{tikzpicture}

    \begin{axis}[
      hide y axis, tick align=outside,
      domain=-3:3, samples=50,
      axis lines*=left, xlabel=$IQ-Werte$, ylabel=$~$,
      height=5cm, width=13cm,
      xtick={-2,-1,0,1,2}, ytick=\empty,
      xticklabels={%
        $70$,
        $85$,
        $100$,
        $115$,
        $130$}      
      ]

      \addplot [thick,black!50!black] {gauss(0,1)};
      \addplot [fill=black!10, domain=-1:1] {gauss(0,1)} \closedcycle;

    \end{axis}
    \end{tikzpicture}

Answer 1

Short answer: Have a look at Christian's answer to this question about multiple y-axes on the same plot and adapt.

Longer answer: keep in mind that a pgfplots axis environment just a special type of tikz node. It has special coordinate systems, and a useful one for drawing over the the plot is the one called axis cs. With this coordinate system you can place TikZ drawing commands on any part of the plot window.

You can achieve a second x-axis by making a second axis environment with the same specifications but no actual function plotted, shifted appropriately. If there were a function plotted it would overlap the first, but without a function all you see are the axes.

\documentclass{article}
\usepackage{pgfplots}
\usepackage{icomma}
\begin{document}
   \pgfmathdeclarefunction{gauss}{2}{%
      \pgfmathparse{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))}%
   }
   \begin{tikzpicture}
      % options common to all axes here
      \pgfplotsset{
         axis x line*=middle, 
         hide y axis, 
         tick align=outside,
         ytick=\empty,
         xmin=-3,xmax=3,
         width=13cm,height=7cm,
         xtick={-2,-1,0,1,2},      
      }

   % main plot
   \begin{axis}[
      samples=50,
      xlabel={IQ-Werte},
      domain=-3:3, 
      xticklabels={%
         $70$,
         $85$,
         $100$,
         $115$,
         $130$}      
      ]
      \addplot [thick,fill=blue!10,domain=-3.1:3.1] {gauss(0,1)} \closedcycle;
      \addplot [fill=blue!20, domain=-1:1] {gauss(0,1)} \closedcycle;
      \draw[thick,arrows={<->}] (axis cs:-1,0.125) -- (axis cs:1,0.125)
         node[pos=0.5,above] {$68,2\%$};
    \end{axis}

    % extra x axis
    \begin{axis}[yshift=-1.5cm,
      xlabel={Prozentr\"ange},
      xticklabels={{$2,3$}, {$15,9$}, {$50$}, {$84,1$}, {$97,7$}}
    ]
    \addplot[draw=none]{1};
    \end{axis}
    \end{tikzpicture}
\end{document}

Notes:

• The icomma package allows for comma decimal separators like you used. You might be implementing that with a different package.
• You used $IQ-Werte$ for the x axis label, but that sets the text within math mode. This means the font shape comes out math italic, there are no ligatures, and the hyphen becomes a minus sign. You probably just want the plain text. Use \textit{IQ-Werte} if you want italic.
• One hack I needed to ensure that the ticks plotted in the second axis were noticed: I plotted a constant function and made it invisible with the draw=none key.
• An earlier version had some white space between the axis and the first plot, as noticed by @maetra. I fixed this by making it a \closedcycle, then extending the domain slightly so that the resulting vertical edges are clipped by the xmin:xmax window.