Probability of z > 1.28: Visualizing the Gaussian Curve

• MHB
• karush
In summary, MHB provides custom tick marks and labels for the Gauss function, as well as the ability to change the height and width of the graph.
karush
Gold Member
MHB
ok I was able to get the graph of P(z>1.28)

\begin{tikzpicture}
%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
%\node [below] at (1.28,0) {$a$};%
\addplot [fill=cyan!30, draw=none, domain=1.28:4] {\gauss{0}{1}} \closedcycle;
\end{axis}
\end{tikzpicture}

but... most guass curves i see are about half this high
and usually only the domain ticks are shown
in this case only 1.28 needs be shown
really don't need what is here on the x-axis
since is basically already understood

also this code was c/p from Overleaf which is very common Latex editor among Universities

MHB has been a great help on this

Last edited:
We can set custom tick marks and/or labels with xtick respectively xticklabels.
And we can change the height with height, in which case we will also want to set the width because otherwise the picture is just scaled.

If we do so, we get:
Code:
\begin{tikzpicture}
%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={1.28},
xticklabels={$a$},
width=10cm,
height=4cm
]
\addplot [fill=cyan!30, draw=none, domain=1.28:4] {\gauss{0}{1}} \closedcycle;
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
%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={1.28},
xticklabels={$a$},
width=10cm,
height=4cm
]
\addplot [fill=cyan!30, draw=none, domain=1.28:4] {\gauss{0}{1}} \closedcycle;
\end{axis}
\end{tikzpicture}

that looks great

i went all over the place to find help with this graph
but the one stop help was here at MHB

1. What is the Probability of z > 1.28?

The probability of z > 1.28 is the area under the standardized normal distribution curve to the right of the z-score 1.28. This can be calculated using a statistical software or by using a z-table.

2. How is the Gaussian Curve visualized?

The Gaussian Curve, also known as the Normal Distribution Curve, is visualized as a bell-shaped curve on a graph. The curve is symmetrical and centered around the mean, with the area under the curve representing the probability of a random variable falling within a certain range.

3. What does a z-score of 1.28 represent?

A z-score of 1.28 represents a data point that is 1.28 standard deviations above the mean in a normal distribution. This means that the data point is relatively far away from the mean and has a low probability of occurring.

4. How is the probability of z > 1.28 calculated?

The probability of z > 1.28 is calculated by finding the area under the curve to the right of the z-score. This can be done using a z-table or a statistical software, or by using the formula P(z > 1.28) = 1 - P(z < 1.28).

5. What is the significance of a z-score > 1.28?

A z-score > 1.28 indicates that the data point is more than 1.28 standard deviations away from the mean, making it a relatively rare occurrence. This can be useful in determining the likelihood of an event or in identifying outliers in a dataset.

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