Gaussian Probability: 1 to 2 in tikz

[karush]

\begin{tikzpicture}[scale=0.6]
%preamble \usepackage{pgfplots}
\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
\begin{axis}[every axis plot post/.append style={
mark=none,samples=50,smooth}, % All plots: 50 samples, smooth, no marks
axis x line*=bottom, % no box around the plot, only x axis
axis y line=none, % the * suppresses the arrow tips
enlargelimits=upper, % extend the axes a bit to the right and top
domain=-4:4, % Default for all plots: from -4:4
xtick={1,2},
xticklabels={$1$,$2$},
width=10cm,
height=4cm]
\addplot [fill=cyan!30, draw=none, domain=1:2] {\gauss{0}{1}} \closedcycle;
\addplot {\gauss{0}{1}};
\end{axis}
\end{tikzpicture}

ok this was for P(1<z<2) scaled the graph to .6
the ultimate answer of course is the area in the domain which I don't know if we can derive from the gauss{}{} function
I tried to put the newcommand quass{}{} in the preamble of Overleaf but it didn't take
also thot since all 12 of homework problem are just graphing P()
be nice just have a newcommand \Pg with arguments but also need code that can be colabortive with Overleaf and MHB

again mega mahalo for all the help

 

[karush]

this is what it looks like in Overleaf...

 

[I like Serena]

I'm afraid that TikZ is not an advanced calculator.
It does not have a function that calculates the area below the Gaussian graph.
And it cannot calculate the integral of a function either.

 

[karush]

ok well that seems to an advantage of desmos over tikz except tikz is much more exotic

 

[I like Serena]

ok well that seem to an advantage of desmos over tikz except tikz is much more exotic

It appears I misunderstood your question somehow.
Desmos does not have such ability either.
Can you clarify what you want?

 

[karush]

well i have graph i wanted
i was just curious about integration function in tikx

but yes desmos has a integration function its under misc in the function menu
i have used it many times

 

[I like Serena]

Well, with a bit of trickery, we can do:
\begin{tikzpicture}[scale=1,
declare function={
gauss(\x,\mean,\sigma) = 1/(\sigma*sqrt(2*pi))*exp(-(\x-\mean)^2/(2*\sigma^2));
normcdf(\x,\m,\s)=1/(1 + exp(-0.07056*((\x-\m)/\s)^3 - 1.5976*(\x-\m)/\s));
},
]
%preamble \usepackage{pgfplots}
\begin{axis}[every axis plot post/.append style={
mark=none,samples=50,smooth}, % All plots: 50 samples, smooth, no marks
axis x line*=bottom, % no box around the plot, only x axis
axis y line=none, % the * suppresses the arrow tips
enlargelimits=upper, % extend the axes a bit to the right and top
domain=-4:4, % Default for all plots: from -4:4
xtick={1,2},
width=10cm,
height=4cm]
\addplot [fill=cyan!30, draw=none, domain=1:2] {gauss(x,0,1)} \closedcycle;
\addplot {gauss(x,0,1)};
\path foreach \y [evaluate=\y as \yeval using {normcdf(\y,0,1)-normcdf(1,0,1)}] in {2} { node[ left ] at (axis cs:{\y},0.05) {\yeval} };
\end{axis}
\end{tikzpicture}

It uses

[declare function={
    normcdf(\x,\m,\s)=1/(1 + exp(-0.07056*((\x-\m)/\s)^3 - 1.5976*(\x-\m)/\s));
}]

to approximate the area under the Gaussian graph.

And it uses evaluate=\y as \yeval using syntax to convert the function call into a value before printing it.

 

[karush]

wow that is pretty cool...