The Normal Distribution is a bell-shaped curve where most data points gather around an average value, showing symmetry and a tendency for values to decrease as they move away from the mean. It’s a fundamental concept in statistics, representing common patterns in various real-world phenomena.

\documentclass[border=10pt]{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.18} \usepgfplotslibrary{fillbetween} \tikzset{every node/.style={font=\sffamily}} \definecolor{linecolor}{HTML}{7AD7F0} \definecolor{grad1}{HTML}{92DFF3} \definecolor{grad2}{HTML}{B7E9F7} \definecolor{grad3}{HTML}{DBF3FA} \definecolor{grad4}{HTML}{F5FCFF} \begin{document} \begin{tikzpicture} \begin{axis}[ width = 17.5cm, height = 7.25cm, xmin = -4.5, xmax = 4.5, ymin = 0, axis x line* = bottom, % the * 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 = {$(\mu-4\sigma)$, $(\mu-3\sigma)$, $(\mu-2\sigma)$, $(\mu-\sigma)$, $\vphantom{(}\mu$, $(\mu+\sigma)$, $(\mu+2\sigma)$, $(\mu+3\sigma)$, $(\mu+4\sigma)$}, % comment this if uncomment above; %commenting this without uncommenting above makes markings integers ] % This draws the vertical lines \pgfplotsinvokeforeach {-3,-2,-1,0,1,2,3} { \draw[linecolor, thin] (axis cs: #1,-1) -- (axis cs: #1,{(1/sqrt(2*pi))*exp((-1/2)*(#1)^2)+0.05}); } % This draws 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)}; % This is necessary for the filling later \path [name path = base] (\pgfkeysvalueof{/pgfplots/xmin},0) -- (\pgfkeysvalueof{/pgfplots/xmax},0); % This labels each section \node at (axis cs: -0.5,0.15) {34\%}; \node at (axis cs: 0.5,0.15) {34\%}; \node at (axis cs: -1.5,0.058) {13.5\%}; \node at (axis cs: 1.5,0.058) {13.5\%}; \node[inner sep=0, pin={[pin edge={lightgray}]90:2.35\%}] at (axis cs: -2.5,0.0) {}; \node[inner sep=0, pin={[pin edge={lightgray}]90:2.35\%}] at (axis cs: 2.5,0.0) {}; \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) {}; % This is where we fill in the regions \addplot [white] fill between [of = dist and base, soft clip = {domain=-4:4}]; \addplot [grad4] fill between [of = dist and base, soft clip = {domain=-3:3}]; \addplot [grad3] fill between [of = dist and base, soft clip = {domain=-2:2}]; \addplot [grad2] fill between [of = dist and base, soft clip = {domain=-1:1}]; \end{axis} \end{tikzpicture} \end{document}

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