(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     14643,        350]
NotebookOptionsPosition[     13925,        330]
NotebookOutlinePosition[     14451,        348]
CellTagsIndexPosition[     14408,        345]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
 RowBox[{"Manipulate", "[", "\[IndentingNewLine]", 
  RowBox[{
   RowBox[{
    RowBox[{"moy", "=", "5"}], ";", "\[IndentingNewLine]", 
    RowBox[{"dist", "=", 
     RowBox[{"NormalDistribution", "[", 
      RowBox[{"moy", ",", "2"}], "]"}]}], ";", "\[IndentingNewLine]", 
    RowBox[{"taille", "=", "10"}], ";", "\[IndentingNewLine]", 
    RowBox[{"z", "=", 
     RowBox[{"Quantile", "[", 
      RowBox[{
       RowBox[{"NormalDistribution", "[", 
        RowBox[{"0", ",", "1"}], "]"}], ",", 
       RowBox[{"1", "-", 
        RowBox[{"alpha", "/", "2"}]}]}], "]"}]}], ";", "\[IndentingNewLine]", 
    RowBox[{"Do", "[", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{
       RowBox[{"sample", "[", "i", "]"}], "=", 
       RowBox[{"RandomReal", "[", 
        RowBox[{"dist", ",", "taille"}], "]"}]}], ",", "\[IndentingNewLine]", 
      RowBox[{"{", 
       RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ";", "\[IndentingNewLine]", 
    RowBox[{"occurrence", "=", 
     RowBox[{"Table", "[", 
      RowBox[{
       RowBox[{"IntervalMemberQ", "[", 
        RowBox[{
         RowBox[{"Interval", "[", 
          RowBox[{"{", 
           RowBox[{
            RowBox[{
             RowBox[{"Mean", "[", 
              RowBox[{"sample", "[", "i", "]"}], "]"}], "-", 
             RowBox[{"z", "*", 
              RowBox[{
               RowBox[{"StandardDeviation", "[", 
                RowBox[{"sample", "[", "i", "]"}], "]"}], "/", 
               RowBox[{"Sqrt", "[", "taille", "]"}]}]}]}], ",", 
            RowBox[{
             RowBox[{"Mean", "[", 
              RowBox[{"sample", "[", "i", "]"}], "]"}], "+", 
             RowBox[{"z", "*", 
              RowBox[{
               RowBox[{"StandardDeviation", "[", 
                RowBox[{"sample", "[", "i", "]"}], "]"}], "/", 
               RowBox[{"Sqrt", "[", "taille", "]"}]}]}]}]}], "}"}], "]"}], 
         ",", "moy"}], "]"}], ",", 
       RowBox[{"{", 
        RowBox[{"i", ",", "n"}], "}"}]}], "]"}]}], ";", "\[IndentingNewLine]", 
    RowBox[{"Nb", "=", 
     RowBox[{"Count", "[", 
      RowBox[{"occurrence", ",", "True"}], "]"}]}], ";", 
    "\[IndentingNewLine]", 
    RowBox[{"Column", "[", 
     RowBox[{"{", "\[IndentingNewLine]", 
      RowBox[{
       RowBox[{"Style", "[", 
        RowBox[{
         RowBox[{"\"\<nombre d'occurrences : \>\"", "<>", 
          RowBox[{"ToString", "@", "Nb"}]}], ",", 
         RowBox[{"{", 
          RowBox[{"\"\<Times\>\"", ",", "18"}], "}"}]}], "]"}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{"Style", "[", 
        RowBox[{
         RowBox[{"\"\<% d'occurrences : \>\"", "<>", 
          RowBox[{"ToString", "[", 
           RowBox[{"Round", "[", 
            RowBox[{
             RowBox[{"Nb", "/", "n"}], "*", "100"}], "]"}], "]"}]}], ",", 
         RowBox[{"{", 
          RowBox[{"\"\<Times\>\"", ",", "16"}], "}"}]}], "]"}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{"Style", "[", 
        RowBox[{
         RowBox[{"\"\<Intervalle de confiance : \>\"", "<>", 
          RowBox[{"ToString", "[", 
           RowBox[{
            RowBox[{"(", 
             RowBox[{"1", "-", "alpha"}], ")"}], "*", "100"}], "]"}]}], ",", 
         RowBox[{"{", 
          RowBox[{"\"\<Times\>\"", ",", "16"}], "}"}]}], "]"}], ",", 
       "\[IndentingNewLine]", 
       RowBox[{"Show", "[", "\[IndentingNewLine]", 
        RowBox[{
         RowBox[{"Graphics", "@", 
          RowBox[{"{", 
           RowBox[{"White", ",", 
            RowBox[{"Line", "[", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"{", 
                RowBox[{"2", ",", "0"}], "}"}], ",", 
               RowBox[{"{", 
                RowBox[{"8", ",", "0"}], "}"}], ",", 
               RowBox[{"{", 
                RowBox[{"8", ",", 
                 RowBox[{"n", "+", "1"}]}], "}"}], ",", 
               RowBox[{"{", 
                RowBox[{"2", ",", 
                 RowBox[{"n", "+", "1"}]}], "}"}]}], "}"}], "]"}]}], "}"}]}], 
         ",", "\[IndentingNewLine]", 
         RowBox[{"Table", "[", 
          RowBox[{
           RowBox[{"Graphics", "@", 
            RowBox[{"{", 
             RowBox[{
              RowBox[{"PointSize", "[", "0.015", "]"}], ",", 
              RowBox[{"Point", "[", 
               RowBox[{"{", 
                RowBox[{
                 RowBox[{"Mean", "[", 
                  RowBox[{"sample", "[", "i", "]"}], "]"}], ",", "i"}], "}"}],
                "]"}]}], "}"}]}], ",", 
           RowBox[{"{", 
            RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", 
         "\[IndentingNewLine]", 
         RowBox[{"Table", "[", "\[IndentingNewLine]", 
          RowBox[{
           RowBox[{"Graphics", "[", 
            RowBox[{"Line", "[", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"{", 
                RowBox[{
                 RowBox[{
                  RowBox[{"Mean", "[", 
                   RowBox[{"sample", "[", "i", "]"}], "]"}], "-", 
                  RowBox[{"z", "*", 
                   RowBox[{
                    RowBox[{"StandardDeviation", "[", 
                    RowBox[{"sample", "[", "i", "]"}], "]"}], "/", 
                    RowBox[{"Sqrt", "[", "taille", "]"}]}]}]}], ",", "i"}], 
                "}"}], ",", 
               RowBox[{"{", 
                RowBox[{
                 RowBox[{
                  RowBox[{"Mean", "[", 
                   RowBox[{"sample", "[", "i", "]"}], "]"}], "+", 
                  RowBox[{"z", "*", 
                   RowBox[{
                    RowBox[{"StandardDeviation", "[", 
                    RowBox[{"sample", "[", "i", "]"}], "]"}], "/", 
                    RowBox[{"Sqrt", "[", "taille", "]"}]}]}]}], ",", "i"}], 
                "}"}]}], "}"}], "]"}], "]"}], "\[IndentingNewLine]", ",", 
           RowBox[{"{", 
            RowBox[{"i", ",", "n"}], "}"}]}], "]"}], ",", 
         RowBox[{"Frame", "\[Rule]", "True"}], ",", 
         RowBox[{"ImageSize", "\[Rule]", 
          RowBox[{"{", 
           RowBox[{"900", ",", "600"}], "}"}]}], ",", 
         RowBox[{"Epilog", "\[Rule]", 
          RowBox[{"{", 
           RowBox[{"Red", ",", "Thick", ",", 
            RowBox[{"Line", "[", 
             RowBox[{"{", 
              RowBox[{
               RowBox[{"{", 
                RowBox[{"moy", ",", "0"}], "}"}], ",", 
               RowBox[{"{", 
                RowBox[{"moy", ",", 
                 RowBox[{"n", "+", "1"}]}], "}"}]}], "}"}], "]"}]}], 
           "}"}]}]}], "\[IndentingNewLine]", "]"}]}], "\[IndentingNewLine]", 
      "}"}], "]"}]}], "\[IndentingNewLine]", ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"n", ",", "10", ",", "\"\<nombre d'\[EAcute]chantillons\>\""}], 
      "}"}], ",", "1", ",", "100", ",", "1"}], "}"}], "\[IndentingNewLine]", 
   ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "alpha", ",", "0.32", ",", 
       "\"\<1-\[Alpha] intervalle de confiance, \[Alpha] =\>\""}], "}"}], ",",
      "0", ",", "1"}], "}"}], ",", "\[IndentingNewLine]", 
   RowBox[{"ContinuousAction", "\[Rule]", "None"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.465039781375*^9, 3.465039883703125*^9}, {
   3.46504005465625*^9, 3.465040172984375*^9}, {3.4650402056875*^9, 
   3.465040252703125*^9}, {3.465040638390625*^9, 3.46504075828125*^9}, 
   3.465040891578125*^9, {3.465041267578125*^9, 3.465041290890625*^9}, {
   3.465041495109375*^9, 3.465041576953125*^9}, {3.465041653328125*^9, 
   3.46504180365625*^9}, {3.46504192625*^9, 3.46504202071875*^9}, {
   3.465042257453125*^9, 3.46504232978125*^9}, {3.46504256784375*^9, 
   3.465042617078125*^9}, {3.46504278246875*^9, 3.465042785734375*^9}, {
   3.46504292153125*^9, 3.46504303675*^9}, {3.465043073625*^9, 
   3.465043082671875*^9}, {3.46504312753125*^9, 3.465043140734375*^9}, {
   3.465043259640625*^9, 3.465043456046875*^9}, {3.465044139140625*^9, 
   3.46504415859375*^9}, {3.465044229171875*^9, 3.465044248703125*^9}, {
   3.46504429603125*^9, 3.465044319546875*^9}, {3.4650443570625*^9, 
   3.46504436521875*^9}, {3.46504443053125*^9, 3.465044446234375*^9}, {
   3.465044488609375*^9, 3.465044675*^9}, {3.46504474675*^9, 
   3.465044749359375*^9}, {3.4650447961875*^9, 3.465044832890625*^9}, {
   3.4650449395625*^9, 3.465044969171875*^9}, {3.592276955836381*^9, 
   3.592276956132781*^9}, 3.81182253077236*^9},
 CellLabel->"In[25]:=",ExpressionUUID->"c078e4c7-0a3c-45d2-9524-c956d63cade7"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`alpha$$ = 0.5, $CellContext`n$$ = 10, 
    Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, 
    Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 
    1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`n$$], 10, "nombre d'\[EAcute]chantillons"}, 1, 100, 
      1}, {{
       Hold[$CellContext`alpha$$], 0.32, 
       "1-\[Alpha] intervalle de confiance, \[Alpha] ="}, 0, 1}}, 
    Typeset`size$$ = {900., {326.8, 332.8}}, Typeset`update$$ = 
    3.8118299691196316`17.33370850937388*^9, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = True}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`alpha$$ = 0.32, $CellContext`n$$ = 10}, 
      "ControllerVariables" :> {}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> ($CellContext`moy = 5; $CellContext`dist = 
        NormalDistribution[$CellContext`moy, 2]; $CellContext`taille = 
        10; $CellContext`z = Quantile[
          NormalDistribution[0, 1], 1 - $CellContext`alpha$$/2]; 
       Do[$CellContext`sample[$CellContext`i] = 
         RandomReal[$CellContext`dist, $CellContext`taille], {$CellContext`i, \
$CellContext`n$$}]; $CellContext`occurrence = Table[
          IntervalMemberQ[
           Interval[{Mean[
               $CellContext`sample[$CellContext`i]] - $CellContext`z (
              StandardDeviation[
                $CellContext`sample[$CellContext`i]]/
              Sqrt[$CellContext`taille]), Mean[
               $CellContext`sample[$CellContext`i]] + $CellContext`z (
               StandardDeviation[
                 $CellContext`sample[$CellContext`i]]/
               Sqrt[$CellContext`taille])}], $CellContext`moy], \
{$CellContext`i, $CellContext`n$$}]; $CellContext`Nb = 
        Count[$CellContext`occurrence, True]; Column[{
          Style[
           StringJoin["nombre d'occurrences : ", 
            ToString[$CellContext`Nb]], {"Times", 18}], 
          Style[
           StringJoin["% d'occurrences : ", 
            ToString[
             Round[($CellContext`Nb/$CellContext`n$$) 100]]], {"Times", 16}], 
          Style[
           StringJoin["Intervalle de confiance : ", 
            ToString[(1 - $CellContext`alpha$$) 100]], {"Times", 16}], 
          Show[
           Graphics[{White, 
             
             Line[{{2, 0}, {8, 0}, {8, $CellContext`n$$ + 1}, {
               2, $CellContext`n$$ + 1}}]}], 
           Table[
            Graphics[{
              PointSize[0.015], 
              Point[{
                Mean[
                 $CellContext`sample[$CellContext`i]], $CellContext`i}]}], \
{$CellContext`i, $CellContext`n$$}], 
           Table[
            Graphics[
             Line[{{Mean[
                  $CellContext`sample[$CellContext`i]] - $CellContext`z (
                 StandardDeviation[
                   $CellContext`sample[$CellContext`i]]/
                 Sqrt[$CellContext`taille]), $CellContext`i}, {Mean[
                  $CellContext`sample[$CellContext`i]] + $CellContext`z (
                  StandardDeviation[
                    $CellContext`sample[$CellContext`i]]/
                  Sqrt[$CellContext`taille]), $CellContext`i}}]], \
{$CellContext`i, $CellContext`n$$}], Frame -> True, ImageSize -> {900, 600}, 
           Epilog -> {Red, Thick, 
             
             Line[{{$CellContext`moy, 0}, {$CellContext`moy, $CellContext`n$$ + 
                1}}]}]}]), 
      "Specifications" :> {{{$CellContext`n$$, 10, 
          "nombre d'\[EAcute]chantillons"}, 1, 100, 
         1}, {{$CellContext`alpha$$, 0.32, 
          "1-\[Alpha] intervalle de confiance, \[Alpha] ="}, 0, 1}}, 
      "Options" :> {ContinuousAction -> None}, "DefaultOptions" :> {}],
     ImageSizeCache->{946., {401., 407.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{
  3.5922772619245186`*^9, 3.7500779349900103`*^9, 3.750077996341653*^9, {
   3.7815371959797134`*^9, 3.781537214444673*^9}, 3.811822502592551*^9, {
   3.8118225411525803`*^9, 3.81182255866453*^9}},
 CellLabel->"Out[25]=",ExpressionUUID->"fcc68d97-b5c1-4c22-9905-d54f04c48471"]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.46504286803125*^9, 
  3.465042918390625*^9}},ExpressionUUID->"59a05aa5-d0d1-45f9-b18b-\
3580f6850060"]
},
WindowSize->{1635.4285714285713`, 853.2857142857142},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
PrivateNotebookOptions->{"VersionedStylesheet"->{"Default.nb"[8.] -> False}},
ShowSelection->True,
FrontEndVersion->"12.1 for Microsoft Windows (64-bit) (March 14, 2020)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"34078e06-26b5-442c-9562-2deceb8a76a2"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 8418, 198, 492, "Input",ExpressionUUID->"c078e4c7-0a3c-45d2-9524-c956d63cade7"],
Cell[8988, 222, 4767, 100, 827, "Output",ExpressionUUID->"fcc68d97-b5c1-4c22-9905-d54f04c48471"]
}, Open  ]],
Cell[13770, 325, 151, 3, 28, "Input",ExpressionUUID->"59a05aa5-d0d1-45f9-b18b-3580f6850060"]
}
]
*)