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

In summary, the conversation is about determining the standard normal (z) curve areas. Specifically, the area under the z curve to the left of $1.75$ is being discussed. It is determined to be approximately $0.959941$ using the given table and input. A tikz from stack exchange is mentioned but it cannot be rendered here.
  • #1
karush
Gold Member
MHB
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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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  • #2
[/S
\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}
POILER]
 

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

1. What is a standard normal (z) curve?

A standard normal (z) curve is a bell-shaped curve that represents the distribution of data in a normal distribution. The curve is centered at 0 and has a standard deviation of 1.

2. How do you determine the area under a standard normal (z) curve?

The area under a standard normal (z) curve can be determined using a z-table or a statistical software. The z-table provides the area between the mean and a specific z-score, while a statistical software can calculate the area between any two z-scores.

3. What does a negative z-score mean?

A negative z-score indicates that the data point is below the mean in a normal distribution. It also represents the number of standard deviations the data point is below the mean.

4. How do you interpret a z-score?

A z-score can be interpreted as the distance between a data point and the mean, measured in standard deviations. A positive z-score indicates that the data point is above the mean, while a negative z-score indicates that the data point is below the mean.

5. Why is it important to know the area under a standard normal (z) curve?

Knowing the area under a standard normal (z) curve is important in statistics because it allows us to calculate probabilities and make inferences about a population based on a sample. It also helps in understanding the distribution of data and identifying outliers.

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