Import work from year 2014-2015
This commit is contained in:
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T_STMG/DS/DST_03/Bilan/bilan.pdf
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T_STMG/DS/DST_03/Bilan/bilan.pdf
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T_STMG/DS/DST_03/Bilan/bilan.tex
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T_STMG/DS/DST_03/Bilan/bilan.tex
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T_STMG/DS/DST_03/Bilan/make bilan.ipynb
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T_STMG/DS/DST_03/Bilan/make bilan.ipynb
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@@ -0,0 +1,417 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Bilan pour les Tsmtg"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 37,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"from texenv import texenv\n",
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"%matplotlib inline"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 38,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"notes = pd.read_excel(\"./../../../notes_tstmg.xls\",sheetname=\"DST_03\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 39,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"notes = notes.T"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 40,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"notes = notes.drop(\"av_arrondi\", axis=1)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On extrait le barème et on l'enlève ainsi que les lignes du tableau qui ne servent à rien."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 41,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"barem = notes[:1]\n",
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"notes = notes[1:-6]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On enlèves les élèves absents"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 42,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"notes = notes[notes[\"DST_03\"].notnull()]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On remplace les réponses NaN par \\NoRep"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 43,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"notes = notes.fillna(\"\\\\NoRep\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On arrondit les points de chacuns des exercices"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 44,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"#notes['Exercice 1'] = notes['Exercice 1'].round(2)\n",
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"#notes['Exercice 2'] = notes['Exercice 2'].round(2)\n",
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"notes[['Exercice 1', 'Exercice 2']] = notes[['Exercice 1', 'Exercice 2']].applymap(lambda x:round(x,2))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On remplace les notes par le code latex"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 45,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"toReplist = ['1.1 (Arbre)', '1.2.a (Décrire évènement)', '1.2.b (Calculer probabilité)', '1.2.c (Calculer probabiltié)', '1.3 (Calculer probabilté)', '1.4 (probabiltié conditionnelle)', '1.5.a (probabilité loi normale)', '1.5.b (probabilité loi normale)', '1.6.a (intervalle 95\\%)', '1.6.b (interprétation)', '2.1 (indice)', '2.2 (indice)', '2.3.a (taux évolution)', '2.3.b (taux évolution moyen)', '2.4 (projection)']"
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]
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},
|
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{
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"cell_type": "code",
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"execution_count": 46,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"def toRepVal(val):\n",
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" if val == \"\\\\NoRep\":\n",
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" return val\n",
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" elif val == 0:\n",
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" return \"\\\\RepZ\"\n",
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" elif val == 1:\n",
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" return \"\\\\RepU\"\n",
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" elif val == 2:\n",
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" return \"\\\\RepD\"\n",
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" elif val == 3:\n",
|
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" return \"\\\\RepT\"\n",
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" else:\n",
|
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" return val"
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]
|
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},
|
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{
|
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"cell_type": "markdown",
|
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"metadata": {},
|
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"source": [
|
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"Pour séléctionner plusieurs colonnes, il faut juste donner entre [] la liste des noms de colones! Facile!"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 47,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
|
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"notes[toReplist] = notes[toReplist].applymap(toRepVal)"
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]
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},
|
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"On entre tout dans le fichier près à compiler!"
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]
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},
|
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{
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"cell_type": "code",
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"execution_count": 56,
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"metadata": {
|
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"collapsed": false
|
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},
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"outputs": [],
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"source": [
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"bilan = texenv.get_template(\"tpl_bilan.tex\")\n",
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"with open(\"./bilan.tex\",\"w\") as f:\n",
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" f.write(bilan.render(eleves = notes, barem = barem))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 48,
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"metadata": {
|
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"collapsed": false
|
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<matplotlib.axes._subplots.AxesSubplot at 0x7f7645bcca58>"
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]
|
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},
|
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"execution_count": 48,
|
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"metadata": {},
|
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"output_type": "execute_result"
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},
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{
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"data": {
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||||
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||||
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||||
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||||
"gUVEZLha45eJPJDGLxq/DN8TkX78jvQcNX6Z/H7LYfwiIiJzQk29tuQdoDXNRL0l7wBZVD+xqKmL\n",
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
"51f9RDKuqZ8IYF/Pen913bht1uRHExGRplaOud1q3g9b7ufkueeAS34E/MJz9fd56DhgxZw/r6EW\n",
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||||
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||||
"/iTfOaNHmtJ+Nzs85rzs137fSdVc/fqZ12MzqH5mfUxznmN945r6vQBOIbkA4FsAfg/ABX3b3Ang\n",
|
||||
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|
||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
"yiYfxVsAPGFm3zOzwwA+i/LvJJqDJH8JAEi+EsB3nPM0RvIilGPISC+qv4zyhGB39T28BsB9JF/h\n",
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||||
"mqqZ/SjrHtX38RGSL/ON1MiFZvav1eXbUf4+rpGm2tTN7GozW2tmr0H5D3T/YWYXTvMxJ8nMvg1g\n",
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||||
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||||
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||||
"4HEE+nCVmf0PydsB3A/gcPXnx3xTjUbyFgBnA3g5yX0o/8X/AwBuI/kHKH+Rx+/6JRxtQP5rUM5B\n",
|
||||
"jwVwd/naiv82s8v9Ug7Wk/1lS8fezG7q2WSuv38H5Uc5rrixepvgTwHM7UnlkNr/QwDXV290+D+U\n",
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||||
"v9589P3ow0ciIt2h/85ORKRD1NRFRDpETV1EpEPU1EVEOkRNXUSkQ9TURUQ6RE1dRKRD1NRFRDrk\n",
|
||||
"/wHnnf0qosURyAAAAABJRU5ErkJggg==\n"
|
||||
],
|
||||
"text/plain": [
|
||||
"<matplotlib.figure.Figure at 0x7f7645bcc2e8>"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"notes[\"DST_03\"].hist(bins = 21)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 51,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"count 21.000000\n",
|
||||
"mean 11.833333\n",
|
||||
"std 3.461695\n",
|
||||
"min 5.500000\n",
|
||||
"25% 10.000000\n",
|
||||
"50% 12.000000\n",
|
||||
"75% 15.000000\n",
|
||||
"max 18.000000\n",
|
||||
"Name: DST_03, dtype: float64"
|
||||
]
|
||||
},
|
||||
"execution_count": 51,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"notes.DST_03.describe()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.4.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
30
T_STMG/DS/DST_03/Bilan/texenv.py
Normal file
30
T_STMG/DS/DST_03/Bilan/texenv.py
Normal file
@@ -0,0 +1,30 @@
|
||||
#!/usr/bin/env python
|
||||
# encoding: utf-8
|
||||
|
||||
import jinja2, os
|
||||
|
||||
# Definition of jinja syntax for latex
|
||||
texenv = jinja2.Environment(
|
||||
block_start_string = '\Block{',
|
||||
# Gros WTF!! Si on le met en maj ça ne marche pas alors que c'est en maj dans le template...
|
||||
block_end_string = '}',
|
||||
variable_start_string = '\Var{',
|
||||
variable_end_string = '}',
|
||||
loader = jinja2.FileSystemLoader(os.path.abspath('.')),
|
||||
extensions = ['jinja2.ext.do']
|
||||
)
|
||||
|
||||
# Filters
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
from pymath.expression import Expression
|
||||
exp = Expression("2/4 + 18")
|
||||
print(do_calculus(exp.simplify()))
|
||||
|
||||
|
||||
|
||||
# -----------------------------
|
||||
# Reglages pour 'vim'
|
||||
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
||||
# cursor: 16 del
|
||||
79
T_STMG/DS/DST_03/Bilan/tpl_bilan.tex
Normal file
79
T_STMG/DS/DST_03/Bilan/tpl_bilan.tex
Normal file
@@ -0,0 +1,79 @@
|
||||
\documentclass{/media/documents/Cours/Prof/Enseignements/2014-2015/Archive/2014-2015/tools/style/classBilan}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/Archive/2014-2015/2014_2015}
|
||||
|
||||
\usepackage{multicol}
|
||||
|
||||
% Title Page
|
||||
\titre{DST 2}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{\TSTMG}
|
||||
\date{18 mars 2015}
|
||||
|
||||
|
||||
\begin{document}
|
||||
|
||||
\Block{for (name, notes) in eleves.iterrows()}
|
||||
\maketitle
|
||||
|
||||
\begin{minipage}{0.5\linewidth}
|
||||
\large
|
||||
\Var{name}
|
||||
\end{minipage}
|
||||
\begin{minipage}{0.3\linewidth}
|
||||
\begin{flushright}
|
||||
\Large \Var{notes['DST_03']} / \Var{barem.DST_03[0]}
|
||||
\end{flushright}
|
||||
\end{minipage}
|
||||
|
||||
\vfill
|
||||
|
||||
\fbox{%
|
||||
\begin{minipage}{0.9\linewidth}
|
||||
\hfill
|
||||
\vspace{2cm}
|
||||
\end{minipage}
|
||||
}
|
||||
|
||||
\vfill
|
||||
|
||||
\scriptsize
|
||||
\begin{multicols}{2}
|
||||
\begin{tabular}{|p{3cm}|c|c|}
|
||||
\hline
|
||||
\rowcolor{highlightbg} Exercices & Barème & Réussite \\
|
||||
\hline
|
||||
\Block{for question in barem.T[1:11].T}
|
||||
\Var{question} & \Var{barem[question][0]} & \Var{notes[question]} \\
|
||||
\hline
|
||||
\Block{endfor}
|
||||
\end{tabular}
|
||||
|
||||
\begin{tabular}{|p{3cm}|c|c|}
|
||||
\hline
|
||||
\rowcolor{highlightbg} Exercices & Barème & Réussite \\
|
||||
\hline
|
||||
\Block{for question in barem.T[11:].T}
|
||||
\Var{question} & \Var{barem[question][0]} & \Var{notes[question]} \\
|
||||
\hline
|
||||
\Block{endfor}
|
||||
\end{tabular}
|
||||
\end{multicols}
|
||||
|
||||
%\begin{tabular}{|p{2cm}|p{2cm}|p{2cm}|p{2cm}|p{2cm}|}
|
||||
% \hline
|
||||
% Pas de réponse & Faux & Peu juste & Partiellement juste & Juste \\
|
||||
% \hline
|
||||
% \NoRep & \RepZ & \RepU & \RepD & \RepT \\
|
||||
% \hline
|
||||
%\end{tabular}
|
||||
\normalsize
|
||||
\pagebreak
|
||||
\Block{endfor}
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
T_STMG/DS/DST_03/DST_03.pdf
Normal file
BIN
T_STMG/DS/DST_03/DST_03.pdf
Normal file
Binary file not shown.
309
T_STMG/DS/DST_03/DST_03.tex
Normal file
309
T_STMG/DS/DST_03/DST_03.tex
Normal file
@@ -0,0 +1,309 @@
|
||||
\documentclass[a4paper,10pt, table]{/media/documents/Cours/Prof/Enseignements/2014-2015/Archive/2014-2015/tools/style/classDS}
|
||||
\usepackage{/media/documents/Cours/Prof/Enseignements/2014-2015/Archive/2014-2015/2014_2015}
|
||||
|
||||
% Title Page
|
||||
\titre{DST 2}
|
||||
% \seconde \premiereS \PSTMG \TSTMG
|
||||
\classe{\TSTMG}
|
||||
\date{Mercredi 18 mars 2015}
|
||||
%\duree{1 heure}
|
||||
%\sujet{%{{infos.subj%}}}
|
||||
% DS DSCorr DM DMCorr Corr
|
||||
\typedoc{DS}
|
||||
|
||||
\printanswers
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
Le barème est donné à titre indicatif, il pourra être modifié.
|
||||
|
||||
\begin{questions}
|
||||
|
||||
\question[9]
|
||||
% Centre étranger juin 2014
|
||||
|
||||
\emph{Les deux parties de l'exercice peuvent être traitées de manière indépendante}
|
||||
|
||||
L'entreprise SAPIQ commercialise des pots de moutarde de 800~g. Un pot est déclaré \textbf{conforme} s'il contient entre 790~g et 810~g de moutarde.
|
||||
|
||||
\medskip
|
||||
|
||||
\textbf{Partie A}
|
||||
\medskip
|
||||
|
||||
L'entreprise dispose de deux machines $m_{1}$ et $m_{2}$.
|
||||
|
||||
La première machine $m_{1}$ produit 60\,\% des pots fabriqués par l'entreprise, le reste de la fabrication étant assuré par la machine $m_{2}$.
|
||||
|
||||
7\,\% des pots produits par la machine $m_{1}$ sont non conformes, alors que la proportion de pots non conformes produits par la la machine $m_{2}$ est de 2\,\% seulement.
|
||||
|
||||
On prélève un pot au hasard dans la production totale.
|
||||
|
||||
On adopte les notations suivantes :
|
||||
|
||||
\setlength\parindent{6mm}
|
||||
\begin{itemize}
|
||||
\item[$\bullet~~$] $M_{1}$ désigne l'évènement \og le pot provient de la machine $m_{1}$. \fg
|
||||
\item[$\bullet~~$] $M_{2}$ désigne l'évènement \og le pot provient de la machine $m_{2}$. \fg
|
||||
\item[$\bullet~~$]C désigne l'évènement : \og le pot est conforme \fg.
|
||||
\end{itemize}
|
||||
\setlength\parindent{0mm}
|
||||
|
||||
Pour tout évènement $E$, on note $p(E)$ sa probabilité et $\overline{E}$ l'évènement contraire de $E$.
|
||||
|
||||
\medskip
|
||||
|
||||
\begin{parts}
|
||||
\part Compléter l'arbre de probabilités fourni en annexe.
|
||||
\part
|
||||
\begin{subparts}
|
||||
\subpart Décrire en une phrase l'évènement $M_1 \cap \overline{C}$.
|
||||
\begin{solution}
|
||||
Cela signifie: "le pot provient de la machine $m_1$ et qu'il n'est pas conforme.
|
||||
\end{solution}
|
||||
\subpart Calculer la probabilité $p\left(M_{1} \cap \overline{C}\right)$.
|
||||
\begin{solution}
|
||||
Cette probabilité correspond à la feuille en vert \TODO{colorier la fleuille} donc
|
||||
\begin{eqnarray*}
|
||||
p\left(M_{1} \cap \overline{C}\right) & = & \frac{60}{100} \times \frac{7}{100} = 0,042
|
||||
\end{eqnarray*}
|
||||
4,2\% des pots produits sont produits par la machine 1 et ne sont pas conformes.
|
||||
\end{solution}
|
||||
\subpart Vérifier que $p\left(M_{2} \cap \overline{C}\right) = 0,008$.
|
||||
\begin{solution}
|
||||
Cette probabilité correspond à la feuille en bleu \TODO{colorier la fleuille} donc
|
||||
\begin{eqnarray*}
|
||||
p\left(M_{2} \cap \overline{C}\right) & = & \frac{40}{100} \times \frac{2}{100} = 0,008
|
||||
\end{eqnarray*}
|
||||
0,8\% des pots produits sont produits par la machine 2 et ne sont pas conformes.
|
||||
\end{solution}
|
||||
\end{subparts}
|
||||
\part Justifier que $p\left(\overline{C}\right) = 0,05$. interpréter cette probabilité.
|
||||
\begin{solution}
|
||||
On cherche à calculer $p(\overline{C})$ ce qui correspond à la probabilité qu'un pot ne soit pas conforme cette probabilité correspond à toutes les feuilles $\overline{C}$ dans l'arbre donc
|
||||
\begin{eqnarray*}
|
||||
p(\overline{C}) & = & p(M_1 \cap \overline{C}) + p(M_2 \cap \overline{C}) = 0,042 + 0,008 = 0,05
|
||||
\end{eqnarray*}
|
||||
|
||||
5\% des pots ne sont pas conformes.
|
||||
|
||||
\end{solution}
|
||||
\part On prélève au hasard un pot parmi les pots non-conformes.
|
||||
|
||||
Déterminer la probabilité qu'il provienne de la machine $m_{2}$.
|
||||
\begin{solution}
|
||||
On veut calculer la probabilité d'avoir un pot venant de la machine $m_2$ parmi les pots non-conformes. On calcule donc
|
||||
\begin{eqnarray*}
|
||||
P_{\overline{C}}(M_2) & = & \frac{p(\overline{C} \cap M_2)}{p(\overline{C})} = \frac{0,008}{0,05} = 0,16
|
||||
\end{eqnarray*}
|
||||
|
||||
|
||||
\end{solution}
|
||||
|
||||
\begin{EnvUplevel}
|
||||
\bigskip
|
||||
|
||||
\textbf{Partie B}
|
||||
|
||||
\medskip
|
||||
|
||||
L' entreprise SAPIQ reçoit un agent commercial vantant les mérites d'une nouvelle machine. La masse de moutarde contenue dans un pot produit par cette nouvelle machine est modélisée par une variable aléatoire $X$. On admet que $X$ suit une loi normale de moyenne $800$ et d'écart type $6$.
|
||||
|
||||
\medskip
|
||||
\end{EnvUplevel}
|
||||
|
||||
\part
|
||||
\begin{subparts}
|
||||
\subpart Calculer $P(X > 810)$.
|
||||
\begin{solution}
|
||||
Comme $X$ suit une loi normale de moyenne $800$ et d'écart-type 6, pour calculer $P(X>810)$ on tape sur sa calculatrice:
|
||||
\begin{center}
|
||||
\verb+normalFRep(810, 10^99, 800,6)+
|
||||
\end{center}
|
||||
Et on obtient $P(X > 810) = 0,048$
|
||||
\end{solution}
|
||||
\subpart Calculer la probabilité arrondie au millième, qu'un pot produit par la nouvelle machine soit conforme.
|
||||
\begin{solution}
|
||||
Pour qu'un pot soit conforme, il faut que sa masse comprise entre 790 et 810g.
|
||||
\begin{eqnarray*}
|
||||
P(790 < X < 810) & = & 0,904
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\end{subparts}
|
||||
|
||||
\part
|
||||
\begin{subparts}
|
||||
\subpart Déterminer l'intervalle centré 800 et contenant 95\% des masses des pots.
|
||||
\begin{solution}
|
||||
L'intervalle contenant 95\% des valeurs et centré en 800 est $\intFF{\mu -2\sigma}{\mu + 2\sigma}$ donc
|
||||
\begin{eqnarray*}
|
||||
\intFF{800 - 2 \times 6}{800 + 2 \times 6} & \mbox{ donc } & \intFF{788}{812}
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{solution}
|
||||
\subpart L'agent commercial avance l'argument suivant : \og $X$ suit une loi normale de moyenne $800$ et d'écart type $6$. Cela signifie que tous les pots produits par notre machine contiennent entre $794$ et $806$~g de moutarde ; ils sont donc tous conformes. \fg
|
||||
|
||||
L'argument de l'agent commercial est-il exact ? Justifier.
|
||||
\begin{solution}
|
||||
D'après la question précédente, 95\% des pots produits contiennent entre 788 et 812 grammes de moutarde. Ce qui signifie que 5\% sont en dehors de cet intervalle et donc non conformes. L'argument de l'agent commercial n'est donc pas exact.
|
||||
|
||||
\end{solution}
|
||||
\end{subparts}
|
||||
|
||||
\end{parts}
|
||||
|
||||
|
||||
\vfill
|
||||
|
||||
\clearpage
|
||||
\question[6]
|
||||
On construit le tableau ci-dessous des indices de la féquentation des campings 4 étoiles ou plus, en prenant comme indice de référence 10à en 2004.
|
||||
|
||||
\begin{tabular}{|c|*{7}{c|}}
|
||||
\hline
|
||||
Année & 2004 & 2005 & 2006 & 2007 & 2008 & 2009 & 2010 \\
|
||||
\hline
|
||||
Fréquentation en miliers de nuitées & 25 156 & & 28 295 & 28897 & 30 063 & 31 212 & 32 014 \\
|
||||
\hline
|
||||
Indice & 100 & 105,22 & 11,48 & & 119,51 & 124,07 & \\
|
||||
\hline
|
||||
\end{tabular}
|
||||
\begin{parts}
|
||||
\part Calculer la fréquentation en 2005.
|
||||
\begin{solution}
|
||||
Fréquentation en 2005:
|
||||
\begin{eqnarray*}
|
||||
\frac{25 156 \times 105,22}{100} & = & 26469
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{solution}
|
||||
\part Calculer l'indice, arrondi au centième, correspondant à l'année 2007.
|
||||
\begin{solution}
|
||||
Indice en 2007
|
||||
\begin{eqnarray*}
|
||||
\frac{28897 \times 100}{25156} & = & 114,87
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{solution}
|
||||
\part
|
||||
\begin{subparts}
|
||||
\subpart Calculer le taux d'évolution global de la fréquentation entre 2004 et 2010. On donnera le résultat en pourcentage à 0,01 près.
|
||||
\begin{solution}
|
||||
Taux d'évolution entre 2004 et 2010
|
||||
\begin{eqnarray*}
|
||||
\frac{y_2 - y_1}{y_1} & = & \frac{32014 - 25156}{25156} = 0,2726 = 27,26\%
|
||||
\end{eqnarray*}
|
||||
\end{solution}
|
||||
\subpart Calculer le taux d'évolution annuel moyen de la fréquentation entre 2004 et 2010.On donnera le résultat en pourcentage à 0,01 près.
|
||||
\begin{solution}
|
||||
On note $t_m$ le taux d'évolution annuel moyen entre 2004 et 2010 (6 évolutions). On a donc
|
||||
\begin{eqnarray*}
|
||||
(1 + t_m)^6 & = & 1 + 0,2726 \\
|
||||
1 + t_m & = & 1,2627^{1/6} \\
|
||||
t_m & = & 1,04099 - 1 = 0,04099 \approx 0,0410 = 4,10\%
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{solution}
|
||||
\end{subparts}
|
||||
\part On suppose que la fréquentation continue à augmenter de 4,10\% par an. Quelle sera alors la fréquentation en 2015?
|
||||
\begin{solution}
|
||||
De 2010 à 2015, il y aura eut 5 évolutions. Donc pour calculer la fréquentation en 2015, on fait
|
||||
\begin{eqnarray*}
|
||||
32 014 \times (1 + \frac{4,1}{100})^5 & = & 39137
|
||||
\end{eqnarray*}
|
||||
La fréquentation sera de 39137 nuités en 2015.
|
||||
\end{solution}
|
||||
\end{parts}
|
||||
|
||||
|
||||
|
||||
\vfill
|
||||
\question[4]
|
||||
Après réalisation d'une enquête, on estime que le temps en minutes, consacré quotidiennement par un élève à faire ses devoirs scolaires, est une variable aléatoire $X$ suivant une loi normale, d'espérance $60$ et d'écart type~$15$.
|
||||
|
||||
L'allure de la courbe de densité de cette loi normale est représentée ci-dessous.
|
||||
|
||||
L'égalité $P(X \leqslant 40) = 0,0912$ est illustrée graphiquement.
|
||||
|
||||
\begin{center}
|
||||
\includegraphics[scale=0.3]{./fig/gaussienne}
|
||||
\end{center}
|
||||
|
||||
\begin{parts}
|
||||
\part La probabilité qu'un élève consacre quotidiennement plus de 40min à faire ses devoirs scolaires est:
|
||||
\begin{oneparchoices}
|
||||
\choice 0,0912
|
||||
\choice 0,8076
|
||||
\choice 0,8
|
||||
\choice 0,9088
|
||||
\end{oneparchoices}
|
||||
|
||||
\part La probabilité qu'un élève consacre quotidiennement plus de $80$~minutes à faire ses devoirs scolaires est:
|
||||
|
||||
\begin{oneparchoices}
|
||||
\choice 0,0912
|
||||
\choice 0,8076
|
||||
\choice 0,8
|
||||
\choice 0,9088
|
||||
\end{oneparchoices}
|
||||
|
||||
\part La probabilité qu'un élève consacre quotidiennement entre 40 et 80 minutes à faire ses devoirs scolaires est:
|
||||
|
||||
\begin{oneparchoices}
|
||||
\choice 0,817
|
||||
\choice 0,95
|
||||
\choice 0,5
|
||||
\choice 0
|
||||
\end{oneparchoices}
|
||||
|
||||
\part La probabilité qu'un élève consacre quotidiennement moins d'une heure à faire ses devoirs scolaires est :
|
||||
|
||||
\begin{oneparchoices}
|
||||
\choice 0,5
|
||||
\choice 0,6
|
||||
\choice 1
|
||||
\choice 0,1368
|
||||
\end{oneparchoices}
|
||||
|
||||
|
||||
\end{parts}
|
||||
|
||||
|
||||
\vfill
|
||||
\end{questions}
|
||||
|
||||
\clearpage
|
||||
|
||||
\Large
|
||||
\begin{center}
|
||||
Annexe \\ À rendre avec le copie \\ Exercice 1
|
||||
|
||||
\hfill
|
||||
|
||||
\begin{tikzpicture}[scale=1.4]
|
||||
\node (root) at (0,0) {$\bullet$};
|
||||
\node (Mu) at (-3, -2) {$M_1$};
|
||||
\node (MuNC) at (-4, -5) {$\overline{C}$};
|
||||
\node (MuC) at (-1, -5) {$C$};
|
||||
\node (Md) at (3, -2) {$M_2$};
|
||||
\node (MdNC) at (1, -5) {$\overline{C}$};
|
||||
\node (MdC) at (4, -5) {$C$};
|
||||
\draw[->] (root) -- (Mu) node[midway, left] {...};
|
||||
\draw[->] (Mu) -- (MuNC) node[midway, left] {...};
|
||||
\draw[->] (Mu) -- (MuC) node[midway, right] {...};
|
||||
\draw[->] (root) -- (Md) node[midway, right] {...};
|
||||
\draw[->] (Md) -- (MdNC) node[midway, left] {...};
|
||||
\draw[->] (Md) -- (MdC) node[midway, right] {...};
|
||||
\end{tikzpicture}
|
||||
\end{center}
|
||||
|
||||
\hfill
|
||||
|
||||
\end{document}
|
||||
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "master"
|
||||
%%% End:
|
||||
|
||||
BIN
T_STMG/DS/DST_03/fig/gaussienne.png
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T_STMG/DS/DST_03/fig/gaussienne.png
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Binary file not shown.
|
After Width: | Height: | Size: 31 KiB |
BIN
T_STMG/DS/DST_03/fig/tbl_indice.png
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BIN
T_STMG/DS/DST_03/fig/tbl_indice.png
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Binary file not shown.
|
After Width: | Height: | Size: 3.7 KiB |
BIN
T_STMG/DS/DST_03/fig/tbl_txEvo.png
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BIN
T_STMG/DS/DST_03/fig/tbl_txEvo.png
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Binary file not shown.
|
After Width: | Height: | Size: 9.1 KiB |
BIN
T_STMG/DS/DST_03/frenquentation.ods
Normal file
BIN
T_STMG/DS/DST_03/frenquentation.ods
Normal file
Binary file not shown.
25
T_STMG/DS/DST_03/index.rst
Normal file
25
T_STMG/DS/DST_03/index.rst
Normal file
@@ -0,0 +1,25 @@
|
||||
Notes sur DST_03
|
||||
################
|
||||
|
||||
:date: 2015-07-01
|
||||
:modified: 2015-07-01
|
||||
:tags: DS, Proba, Information_chifree
|
||||
:category: T_STMG
|
||||
:authors: Benjamin Bertrand
|
||||
:summary: Pas de résumé, note créée automatiquement parce que je ne l'avais pas bien fait...
|
||||
|
||||
|
||||
|
||||
`Lien vers tbl_txEvo.ods <tbl_txEvo.ods>`_
|
||||
|
||||
`Lien vers DST_03.pdf <DST_03.pdf>`_
|
||||
|
||||
`Lien vers frenquentation.ods <frenquentation.ods>`_
|
||||
|
||||
`Lien vers DST_03.tex <DST_03.tex>`_
|
||||
|
||||
`Lien vers fig/gaussienne.png <fig/gaussienne.png>`_
|
||||
|
||||
`Lien vers fig/tbl_txEvo.png <fig/tbl_txEvo.png>`_
|
||||
|
||||
`Lien vers fig/tbl_indice.png <fig/tbl_indice.png>`_
|
||||
BIN
T_STMG/DS/DST_03/tbl_txEvo.ods
Normal file
BIN
T_STMG/DS/DST_03/tbl_txEvo.ods
Normal file
Binary file not shown.
Reference in New Issue
Block a user