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Source LaTeX icone Fiche-Calculatrice-Casio-Loi-normale



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Description
Fiche calculatrice Casio: calculs avec la loi normale
Niveaux
Terminale: S, ES, STI2D, STMG
Mots clé
calculatrice, Casio, loi normale, fiche de cours
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\newcommand{\TITLE}{Calculs Casio pour la loi normale $\mathcal{N}(\mu;\sigma^2)$}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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}

%\psset{unit=2cm}
\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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