normaldist-1

\documentclass[tikz,margin=8pt,convert={svg,command=\unexpanded{{inkscape\space --pdf-poppler\space --export-type="svg"\space --pages=1\space -o\space \outfile\space \infile}}}]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}
%
\definecolor{fillcolor}{HTML}{8A5CF5}
%
\begin{document}
\begin{tikzpicture}[white]
	\begin{axis}[
		width=17.5cm,
		height=7.25cm,
		xmin=-4.5, xmax=4.5,
		ymin=0,
		axis x line* = bottom, % asterisk suppresses the arrow tips
		hide y axis,
		xtick={-4,...,4},
		% xtick={0},
		% tick label style={color=white}, % uncomment this line and change all other xtick tags to remove x-axis markings
		xtick align=outside,
		xticklabels={$(\mu-4\sigma)$, $(\mu-3\sigma)$, $(\mu-2\sigma)$, $(\mu-\sigma)$, $\mu$, $(\mu+\sigma)$, $(\mu+2\sigma)$, $(\mu+3\sigma)$, $(\mu+4\sigma)$}, % comment this if uncomment above; commenting this without uncommenting above makes markings integers
		]
		
		% Draw the vertical lines:
		\pgfplotsinvokeforeach {-3,-2,-1,0,1,2,3} {
		\draw[fillcolor, thin] (axis cs: #1,-1) -- (axis cs: #1,{(1/sqrt(2*pi))*exp((-1/2)*(#1)^2)+0.05});
		}

		% Draw the main curve:
		\addplot [
			domain = -4.5:4.5, 
			samples = 251, 
			color = black,
			name path = dist
			]
			{(1/sqrt(2*pi))*exp((-1/2)*x^2)};
		
		% Store path as boundary for filling later:
		\path [name path = base] (\pgfkeysvalueof{/pgfplots/xmin},0) -- (\pgfkeysvalueof{/pgfplots/xmax},0);
		
		% Label each section:
		\node at (axis cs: -0.5,0.15) {$34\%$};
		\node at (axis cs: 0.5,0.15) {$34\%$};
		\node at (axis cs: -1.5,0.07) {$13.5\%$};
		\node at (axis cs: 1.5,0.07) {$13.5\%$};
		\node[inner sep=0, pin={[pin edge={lightgray}]90:$2.35\%$}] at (axis cs: -2.5,0.01) {};
		\node[inner sep=0, pin={[pin edge={lightgray}]90:$2.35\%$}] at (axis cs: 2.5,0.01) {};
		\node[inner sep=0, pin={[pin edge={lightgray}]90:$0.15\%$}] at (axis cs: -3.5,0) {};
		\node[inner sep=0, pin={[pin edge={lightgray}]90:$0.15\%$}] at (axis cs: 3.5,0) {};
		
		% Fill in the regions:
		\addplot [fillcolor,opacity=0.4] fill between [of=dist and base, soft clip = {domain=-4:4}];
		\addplot [fillcolor,opacity=0.4] fill between [of=dist and base, soft clip = {domain=-3:3}];
		\addplot [fillcolor,opacity=0.4] fill between [of=dist and base, soft clip = {domain=-2:2}];
		\addplot [fillcolor,opacity=0.4] fill between [of=dist and base, soft clip = {domain=-1:1}];
	\end{axis}
\end{tikzpicture}
\end{document}