\begin{exercice}[Campagne publicitaire][\algo]
Un grossiste affiche sur ses plaquettes :\\ \og \upc{86} de notre thé est garanti sans trace de pesticides \fg. \\L'inspectrice de la DGCCRF souhaite étudier la validité de l'affirmation. Elle prélève 100 boîtes au hasard du stock du grossiste et en trouve 26 avec des traces de pesticides. On suppose que la proportion de boîtes sans trace de pesticides est bien égale à \u{0,86} du stock du grossiste. À l'aide d'un logiciel, on simule 200 prélèvements de 100 boîtes. Le graphique ci-dessous présente la fréquence en \upc{} des boîtes de thé ne contenant pas de pesticides pour chaque échantillon .
\begin{center}
\begin{tikzpicture}[yscale=0.1,xscale=0.03, general]
 \draw[quadrillage, ystep=5, xstep=200] (0,70) grid (200,100) ;
 \axeX[70]{0}{210}{0,50,100,150,200}
 \axeY{70}{100}{70,75,80,85,90,95}
% \draw[axe] (-1,72)--(210,72);
% \draw[axe] (0,72)--(0,102);
% \foreach \x in {0,50,100,150,200} \draw (\x,71) node[below]{\footnotesize \x}--(\x,73) ;
% \foreach \y/\n in {72/70,77/75,82/80,87/85,92/90,97/95} {\draw (0,\y) node[left] {$0,\n$} ;\draw (0,\y) node {$+$} ;}
\draw[A1,tres epais, line cap=butt] (0,88)--(200,88);
\draw[B1prime, tres epais, line cap=butt] (0,78)--(200,78);
\draw[B1prime, tres epais, line cap=butt] (0,98)--(200,98);

\foreach \x/\y in {1/91,2/87,3/86,4/90,5/87,6/86,7/80,8/92,9/90,10/88,11/88,12/91,13/82,14/85,15/88,
16/88,17/82,18/87,19/93,20/97,21/86,22/88,23/85,24/88,25/91,26/85,27/89,28/87,29/90,30/89,31/90,32/98,33/87,34/88,35/93,36/86,37/86,38/93,39/83,40/88,41/87,42/86,43/88,44/74,45/93,46/93,47/85,48/89,49/92,50/87,51/88,52/90,53/89,54/93,55/89,56/90,57/86,58/93,59/85,60/89,61/87,62/86,63/84,64/93,65/88,66/85,67/83,68/86,69/93,70/82,71/91,72/85,73/92,74/92,75/92,76/85,77/89,78/95,79/83,80/86,81/91,82/88,83/77,84/94,85/99,86/90,87/90,88/89,89/87,90/89,91/91,92/88,93/82,94/89,95/89,96/90,97/88,98/88,99/91,100/89,101/90,102/82,103/88,104/84,105/83,106/86,107/88,108/85,109/90,110/92}{\draw (\x,\y) node {\footnotesize $\bullet$};} 
\foreach \x/\y in {
111/92,112/89,113/90,114/92,115/89,116/92,117/86,118/90,119/78,120/90,121/88,122/85,123/87,124/86,125/89,126/88,127/91,128/88,129/86,130/91,131/91,132/93,133/91,134/86,135/88,136/90,137/83,138/92,139/90,140/87,141/87,142/84,143/85,144/86,145/91,146/92,147/93,148/88,149/90,150/86,151/86,152/89,153/89,154/86,155/87,156/89,157/93,
 158/86,159/87,160/93,161/93,162/86,163/88,164/92,165/91,166/89,167/91,168/88,
 169/91,170/89,171/83,172/89,173/88,174/87,175/94,176/85,177/84,178/91,179/90,180/90,181/93,182/78,183/88,184/82,185/92,186/99,187/91,188/90,189/92,190/87,191/82,192/87,193/88,194/89,195/91,196/87,197/85,198/90,199/88,200/90} {\draw (\x,\y) node {\footnotesize $\bullet$};}  
\end{tikzpicture}
\end{center}
 \vspace{-1.5em}
 \begin{enumerate}
\item Combien de fréquences n'appartiennent pas à l'intervalle $[0,76;0,96]$? Interpréter.
\item L'inspectrice peut-elle décider, au seuil de 95\%, que la publicité est mensongère ?
\item Proposer un algorithme simulant cette situation. 
\end{enumerate}

\end{exercice}
