\documentclass[varwidth=true, border=4pt]{article}
\usepackage[active,tightpage]{preview}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepackage{helvet}
\usepackage[eulergreek]{sansmath}

\def\cdf(#1)(#2)(#3){0.5*(1+(erf((#1-#2)/(sqrt(#3*2)))))}%
% to be used: \cdf(x)(mean)(variance)

\DeclareMathOperator{\CDF}{cdf}

\pgfplotsset{
tick label style = {font=\sansmath\sffamily},
every axis label/.append style={font=\sffamily\footnotesize},
}

\begin{document}
\begin{preview}
\begin{tikzpicture}
    \begin{axis}[
        width=13.5cm,
        height=8.625cm,
        % Grid
        grid = major,
        grid style={black, thin},
        % size
        xmin=-5.25,  % start the diagram at this x-coordinate
        xmax= 5.25,  % end   the diagram at this x-coordinate
        ymin=-0.05,  % start the diagram at this y-coordinate
        ymax= 1.05,  % end   the diagram at this y-coordinate
        % Legende
        legend pos=north west,
        legend style={font=\footnotesize},
        % Ticks
        tick align=inside,
        minor tick num=3,
        minor tick style={thick},
        yticklabel style={
            /pgf/number format/precision=1,
            /pgf/number format/fixed,
            /pgf/number format/fixed zerofill},
        % Axis
        axis line style = very thick,
        xlabel=$x$,
        x label style={at={(axis description cs:0.5,0)},
                       anchor=north,
                       font=\boldmath\Large},
        ylabel=$\Phi_{\mu, \sigma^2}(x)$,
        y label style={at={(axis description cs:0.05,0.5)},
                       anchor=south,
                       font=\boldmath\Large},
        ]
        \addplot[domain=-5.25:5.25,smooth,blue!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(0.2)};
        \addplot[domain=-5.25:5.25,smooth,red!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(1.0)};
        \addplot[domain=-5.25:5.25,smooth,yellow!80!black,ultra thick,samples=200,] gnuplot{\cdf(x)(0)(5)};
        \addplot[domain=-5.25:5.25,smooth,green!70!black,ultra thick,samples=200,] gnuplot{\cdf(x)(-2)(0.5)};
      \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 0.2$}
      \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 1.0$}
      \addlegendentry{$\mu=\hphantom{-}0,\quad \sigma^2 = 5.0$}
      \addlegendentry{$\mu=-2,\quad \sigma^2 = 0.5$}
    \end{axis} 
\end{tikzpicture}
\end{preview}
\end{document}