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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\usepackage{wasysym}
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\author{Benjamin Bertrand}
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\title{Intervalle de confiance}
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\date{Décembre 2020}
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\tribe{Enseignements Scientifiques}
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\newcommand\cours{%
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\begin{bclogo}[barre=none, arrondi=0.1, logo=]{Cours: Intervalle de confiance}
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\begin{minipage}{0.6\linewidth}
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On cherche à estimer $p$ la proportion d'un caractère d'une population. Pour cela, on fait un échantillon de $n$ individus de cette population et l'on calcule $f$ la fréquence (proportion) du caractère dans cet échantillon.
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On peut définir \textbf{l'intervalle de confiance à 95\%}
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\[
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IC_{95\%} = \intFF{f - \frac{1}{\sqrt{n}}}{f+\frac{1}{\sqrt{n}}}
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\]
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Alors $p$ est dans cet intervalle avec une probabilité de 95\%.
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\end{minipage}
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\hfill
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\begin{minipage}{0.3\linewidth}
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\includegraphics[scale=0.6]{./fig/confiance}
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\end{minipage}
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\end{bclogo}
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}
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\begin{document}
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\cours
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\cours
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\cours
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\cours
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\cours
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\end{document}
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\documentclass[a5paper,10pt]{article}
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\usepackage{myXsim}
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\usepackage{wasysym}
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\author{Benjamin Bertrand}
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\title{Intervalle de confiance}
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\date{Décembre 2020}
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\tribe{Enseignements Scientifiques}
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\setlength{\columnseprule}{0pt}
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\geometry{left=10mm,right=10mm, top=5mm, bottom=5mm}
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\begin{document}
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\maketitle
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\begin{doc}{Deux phénotypes de l’épervier strié}
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% Issu du livre scolaire
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L’épervier strié est un poisson qui vit dans les récifs coralliens. Il existe sous deux phénotypes : sombre et clair. Un recensement des formes claires et sombres a été effectué le long de cinquante-quatre transects, de la surface jusqu’au fond du lagon.
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\begin{tabular}{|p{2cm}|p{2cm}|p{2cm}|}
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\hline
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Nombre de Poissons & Profondeur < 5m & Profondeur > 5m \\
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\hline
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Sombre & 538 & 20 \\
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\hline
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Clairs & 310 & 238 \\
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\hline
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\end{tabular}
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\medskip
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Peut-on affirmer que les poissons sombres préfèrent vivre proche de la surface?
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\end{doc}
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\begin{doc}{Sondage d'élection}
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Deux candidats se présentent à une élection. Un sondage est commandé pour chercher à prédire les résultats. Il est fait sur 1302 électeurs. 629 déclarent qu'ils projettent de voter pour le candidat A et le reste pour le candidat B.
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\medskip
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Peut-on affirmer que le candidat $A$ a aucune chance d'être élu?
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\end{doc}
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\begin{doc}{Compétition entre établissements}
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Trois établissements scolaires revendiquent être les meilleurs pour préparer leurs élèves au bac. Voici leurs résultats pour l'année dernière.
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\begin{tabular}{|c|c|c|}
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\hline
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Nombre d'élèves & Reçut & Refusé \\
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\hline
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Lycée A & 40 & 13 \\
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\hline
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Lycée B & 87 & 36 \\
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\hline
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Lycée C & 140 & 16 \\
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\hline
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\end{tabular}
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\medskip
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Peut-on affirmer qu'un établissement est meilleur qu'un autre?
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\end{doc}
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\end{document}
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x="55.827282"
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id="tspan849">f connue et n connue</tspan></text>
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|
Before Width: | Height: | Size: 14 KiB |
@ -33,17 +33,10 @@ Simulation de la variation de la taille de la population trouvée avec cette mé
|
|||||||
|
|
||||||
Estimation d'une proportion d'une population avec l'échantillonnage.
|
Estimation d'une proportion d'une population avec l'échantillonnage.
|
||||||
|
|
||||||
.. image:: ./4B_confiance.pdf
|
|
||||||
:height: 200px
|
|
||||||
:alt: Cours sur l'intervalle de confiance
|
|
||||||
|
|
||||||
.. image:: ./4E_confiance.pdf
|
|
||||||
:height: 200px
|
|
||||||
:alt: Documents pour travailler l'intervalle de confiance
|
|
||||||
|
|
||||||
Étape 4: Hardy-Weinberg
|
Étape 4: Hardy-Weinberg
|
||||||
=======================
|
=======================
|
||||||
|
|
||||||
|
|
||||||
.. image:: ./3E_Hardy_Weinberg.pdf
|
.. image:: ./3E_Hardy_Weinberg.pdf
|
||||||
:height: 200px
|
:height: 200px
|
||||||
:alt: Étude du modèle d'équilibre de HW
|
:alt: Étude du modèle d'équilibre de HW
|
||||||
|
|||||||
Binary file not shown.
@ -1,110 +0,0 @@
|
|||||||
\documentclass[a4paper,10pt]{article}
|
|
||||||
\usepackage{myXsim}
|
|
||||||
|
|
||||||
% Title Page
|
|
||||||
\title{DS 4}
|
|
||||||
\tribe{Terminale STI2D}
|
|
||||||
\date{14 décembre 2020}
|
|
||||||
\duree{30min}
|
|
||||||
|
|
||||||
\pagestyle{empty}
|
|
||||||
\newcommand{\reponse}[1]{%
|
|
||||||
\begin{bclogo}[barre=none, logo=]{Réponse}
|
|
||||||
\vspace{#1}
|
|
||||||
\end{bclogo}
|
|
||||||
}
|
|
||||||
|
|
||||||
\begin{document}
|
|
||||||
\maketitle
|
|
||||||
|
|
||||||
Le barème est donné à titre indicatif, il pourra être modifié. Les questions plus difficiles sont marqués du symbole (*).
|
|
||||||
|
|
||||||
\begin{exercise}[subtitle={Complexes}, points=4]
|
|
||||||
\noindent
|
|
||||||
\begin{minipage}{0.6\textwidth}
|
|
||||||
\begin{enumerate}
|
|
||||||
\item Soit $z_1 = 4 - 4\sqrt{3}i$. Calculer son module et son argument.
|
|
||||||
\reponse{5cm}
|
|
||||||
\end{enumerate}
|
|
||||||
\end{minipage}
|
|
||||||
\hfill
|
|
||||||
\begin{minipage}{0.35\textwidth}
|
|
||||||
\begin{tikzpicture}[baseline=(a.north), xscale=0.6, yscale=0.6]
|
|
||||||
\tkzInit[xmin=-5,xmax=5,xstep=1,
|
|
||||||
ymin=-5,ymax=5,ystep=1]
|
|
||||||
\tkzGrid
|
|
||||||
\draw (1, 0) node [below right] {1};
|
|
||||||
\draw (0, 1) node [above left] {$i$};
|
|
||||||
\draw [->, very thick] (-5, 0) -- (5, 0);
|
|
||||||
\draw [->, very thick] (0, -5) -- (0, 5);
|
|
||||||
%\tkzAxeXY
|
|
||||||
\foreach \x in {0,1,...,5} {
|
|
||||||
% dots at each point
|
|
||||||
\draw[black] (0, 0) circle(\x);
|
|
||||||
}
|
|
||||||
\end{tikzpicture}
|
|
||||||
\end{minipage}
|
|
||||||
|
|
||||||
\begin{enumerate}
|
|
||||||
\setcounter{enumi}{1}
|
|
||||||
\item Soit $z_2$ le complexe de module $r = 2$ et d'argument $\theta = \dfrac{5\pi}{6}$
|
|
||||||
\reponse{2cm}
|
|
||||||
\item Placer ces deux points dans le plan complexe.
|
|
||||||
\item (*) Placer dans le plan complexe le point $\ds z = \frac{2i+3}{1 - i}$
|
|
||||||
\reponse{3cm}
|
|
||||||
\end{enumerate}
|
|
||||||
\end{exercise}
|
|
||||||
|
|
||||||
\begin{exercise}[subtitle={Intégration}, points=4]
|
|
||||||
\begin{enumerate}
|
|
||||||
\item Calculer la primitive des deux fonctions suivantes
|
|
||||||
\begin{enumerate}
|
|
||||||
\item $f(x) = 4x^3 - 6x^2 + 12$
|
|
||||||
\reponse{2cm}
|
|
||||||
\pagebreak
|
|
||||||
\item $g(x) = 3x(x - x^2 + 1)$
|
|
||||||
\reponse{2cm}
|
|
||||||
|
|
||||||
\end{enumerate}
|
|
||||||
\item On note $f(x) = 0.4x^2 + \cos(x)$ et $F(x) = 0.1x^3 + \sin(x)$ une primitive de $f(x)$.
|
|
||||||
\begin{enumerate}
|
|
||||||
\item Calculer la quantité $\ds \int_1^3 0.4x^2 + \cos(x) \; dx$
|
|
||||||
\reponse{3cm}
|
|
||||||
|
|
||||||
\item Représenter sur le graphique à quoi correspond cette quantité.
|
|
||||||
|
|
||||||
\begin{tikzpicture}[baseline=(a.north), xscale=1.5, yscale=0.5]
|
|
||||||
\tkzInit[xmin=-5,xmax=5,xstep=1,
|
|
||||||
ymin=0,ymax=5,ystep=1]
|
|
||||||
\tkzGrid
|
|
||||||
\tkzAxeXY
|
|
||||||
\tkzFct[domain=-4:4,color=red,very thick]%
|
|
||||||
{ 0.4*\x**2 + cos(\x) };
|
|
||||||
\end{tikzpicture}
|
|
||||||
\end{enumerate}
|
|
||||||
\end{enumerate}
|
|
||||||
\end{exercise}
|
|
||||||
|
|
||||||
\begin{exercise}[subtitle={Vrai/faux}, points=2]
|
|
||||||
Pour chacune des quatre affirmations suivantes, indiquer si elle est vraie ou fausse, en justifiant la réponse.
|
|
||||||
Il est attribué un point par réponse exacte correctement justifiée.
|
|
||||||
Une réponse non justifiée n’est pas prise en compte.
|
|
||||||
Une absence de réponse n’est pas pénalisée.
|
|
||||||
\begin{enumerate}
|
|
||||||
\item L'accélération gravitationnelle se calcule avec la formule $g=\dfrac{G\times m}{r^2}$ où $m$ est la masse, $r$ le rayon et $G$ la constante de gravitation.
|
|
||||||
|
|
||||||
\textbf{Affirmation 1:} Pour calculer la masse, on peut utiliser la formule $m = \dfrac{g\times G}{r^2}$
|
|
||||||
\reponse{2cm}
|
|
||||||
|
|
||||||
\item (*) \textbf{Affirmation 2:} $F(x) = \dfrac{1}{x}\sin(x)$ est une primitive de $f(x) = \dfrac{-1}{x^2}\sin(x) + \dfrac{\cos(x)}{x}$
|
|
||||||
\reponse{2cm}
|
|
||||||
\end{enumerate}
|
|
||||||
\end{exercise}
|
|
||||||
|
|
||||||
\end{document}
|
|
||||||
|
|
||||||
%%% Local Variables:
|
|
||||||
%%% mode: latex
|
|
||||||
%%% TeX-master: "master"
|
|
||||||
%%% End:
|
|
||||||
|
|
||||||
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