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\newcommand{\TITLE}{Calculs Casio pour la loi normale $\mathcal{N}(\mu;\sigma^2)$}
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\begin{document}
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Soit $X$ une v.a. qui suit la loi $\mathcal{N}(\mu;\sigma^2)$.
\vspace{-0.3cm}
\paragraph{Calcul "direct"} \
\vspd
\Prog[\!\!Casio: Graph 35$+$ et modèles supérieurs]{\textwidth}{
Menu \texttt{STAT}, puis \texttt{DIST},
et enfin \texttt{NORM}\\%[0.2cm]
$\bullet$ Calcul de $P(a\leqslant X\leqslant b)$ $\to$
\texttt{Ncd} {\sl (Normal, cumulative distribution)} \\
avec pour valeurs:
\begin{tabular}[t]{ll}
\texttt{Lower} &: a \\
\texttt{Upper} &: b \\
\texttt{$\sigma$} &: $\sigma$ \\
\texttt{$\mu$} &: $\mu$
\end{tabular}\\
puis \texttt{Calc (F1)} \dots\\[0.2cm]
$\bullet$ Calcul de $P(X\leqslant b)$: \\
on peut procéder de même, avec la borne inférieure
\texttt{Lower} : $-1${\scriptsize E}$+99$
\vspace{-0.4cm}
}
\vspd
\paragraph{Calcul "inverse"} \
On cherche à déterminer la valeur du réel $a$ tel que
$P(X\leqslant a)=p$, la probabilité $p$ étant connue.
\vspd
\Prog[\!\!Casio: Graph 35$+$ et modèles supérieurs]{\textwidth}{
Menu \texttt{STAT}, puis \texttt{DIST},
et enfin \texttt{NORM}\\
$\bullet$ Calcul de $a$ tel que $P(X\leqslant a)=p$
$\to$ \texttt{InvN} \ {\sl (Inverse Normal)}\\
avec pour valeurs:
\begin{tabular}[t]{ll}
\texttt{Tail} &: Left \\
\texttt{Area} &: p \\
\texttt{$\sigma$} &: $\sigma$ \\
\texttt{$\mu$} &: $\mu$
\end{tabular}\\
puis \texttt{Calc (F1)} \dots
\vspace{-0.4cm}
}
\vspace{1cm}
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\Att{
Il reste (très) important de savoir se ramener à la loi normale cenrée
réduite $\mathcal{N}(0;1)$ par la transformation
$Y=\dfrac{X-\mu}{\sigma}$.
\vsp
En effet, l'énoncé peut demander explicitement d'utiliser des valeurs
de la fonction $\Pi$, fonction de répartition de la loi
$\mathcal{N}(0;1)$.
\vsp
On peut aussi avoir à chercher $\mu$ ou $\sigma$, dans quels cas la
calculatrice n'est pas utilisable directement (car nécessite justement
la connaissance de $\mu$ et $\sigma$\dots)
}
\end{document}
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