MHB -7.64 Determine the following standard normal (z) curve areas:

AI Thread Summary
The discussion focuses on calculating the area under the standard normal (z) curve to the left of z = 1.75, which is approximately 0.959941 based on the provided z-table value. A user mentions difficulty rendering a TikZ diagram from Stack Exchange in their current environment, despite it working in Overleaf. The conversation emphasizes the importance of understanding z-scores and their corresponding areas in statistical analysis. The need for accurate graphical representation in statistical discussions is also highlighted. Overall, the thread illustrates the intersection of statistical calculations and technical challenges in visualizing data.
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Determine the following standard normal (z) curve areas:

Determine the following standard normal (z) curve areas:

a. The area under the z curve to the left of $1.75$
from table $5\ \textit{$z^{*}$} =1.7 \textit{ col } .05 = .9599$
$\textit{ \textbf{$W\vert A$} input } (z\le 1.75)\approx 0.959941$

ok I found this tikz from stack exchange but I can't get it to render here

\begin{tikzpicture}[>={Stealth[length=6pt]},
declare function={g(\x)=2*exp(-\x*\x/3);
xmax=3.5;xmin=-3.4;x0=1.5;ymax=2.75;}]
\draw[gray!50] (-3.7,0) edge[->] (4,0) foreach \X in {-3.5,-3,...,3}
{(\X,0) -- ++ (0,0.1)} (0,0) edge[->] (0,ymax);
\fill[gray!60] plot[domain=x0:xmax,samples=15,smooth] (\x,{g(\x)}) -- (xmax,0) -| cycle;
\draw[thick] plot[domain=xmin:xmax,samples=51,smooth] (\x,{g(\x)});
\path (4,0) node[below]{$x$} (x0,0) node[below]{3};
{$Z_{\mathrlap{1-\alpha}}$}
(0,ymax) node{$f(x)$};\
end{tikzpicture}
however it rendered in overleaf...
 
Last edited:
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\documentclass{article}
\usepackage{pgfplots}
\begin{document}

\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma

\begin{tikzpicture}
\begin{axis}[every axis plot post/.append style={
mark=none,domain=-2:3,samples=50,smooth}, % All plots: from -2:2, 50 samples, smooth, no marks
axis x line*=bottom, % no box around the plot, only x and y axis
axis y line*=left, % the * suppresses the arrow tips
enlargelimits=upper] % extend the axes a bit to the right and top
\addplot {\gauss{0}{0.5}};
\addplot {\gauss{1}{0.75}};
\end{axis}
\end{tikzpicture}
\end{document}
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