{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 0 128 128 128 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output " -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 11 128 0 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 11 0 128 128 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 5 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(stats): with(statevalf):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "mu:=1000;\nn:=20: sigma:=15/sqrt(n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG\"%+5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%& sigmaG,$*(\"\"$\"\"\"\"\"#!\"\"\"\"&#F(F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "f1:=statevalf[cdf,normald[mu,sigma]]:\nf2:=stateva lf[icdf,normald[mu,sigma]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "P:=1-f1(1005);\n" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"PG$\"*Sc=!o!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "# 1. Aufgabe, Bereich um den Erwartungsw ert zu vorgegebener Sicherheitswahrscheinlichkeit gesucht " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "Sicherheit:=0.95:\nlinke_Gre nze:=f2((1-Sicherheit)/2); # gr\366\337ergleich, aufrunden" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%-linke_GrenzeG$\"+43EM**!\"(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "rechte_Grenze:=2*mu-linke_Gr enze;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.rechte_GrenzeG$\"+>Rd15!\" '" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "\n # 2. Aufgabe Lie gt eine signifikante Abweichung eines Testergebnisses (Durchschnitt) v or?\n mu:=9700; # Putengewicht\n sigma:=320;\n n:=500; # \+ Anzahl der Puten f\374r die Durchschnittsberechnung\n sigma_x_quer:=si gma/sqrt(n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG\"%+(*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG\"$?$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"$+&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-sigma_x_querG, $*(\"#K\"\"\"\"\"&!\"\"F)#F(\"\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "f1:=statevalf[cdf,normald[mu,sigma_x_quer]]:\n\nX_que r:=9729:\n1-f1(X_quer); # Fehler 1. Art " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*:.g8#!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 " # 3. Aufgabe Erw artungswert bestimmen, Standardabweichung und eine Wahrscheinlichkeit \+ sind gegeben" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 214 " sigma:=10 0; f2:=statevalf[icdf,normald[0,1]]:\n\n n:=400: p:=0.025: # P(X<=n )<=p \n # Hersteller behauptet z. B., dass h\366chstens p=2,5% der Bi rnen k\374rzer als n=400 Stunden halten.\n k:=f2(p); # kleinergleic h \n" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG\"$+ \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG$!+&)R'*f>!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "# mittlere Lebensdauer muss mindes tens sein:\n solve( (n-m)/sigma=k,m); # gr\366\337ergleich, aufru nden" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+&)R'*ff!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "\n# 4. Aufgabe Sigma bestimmen, E rwartungswert und eine Wahrscheinlichkeit gegeben" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 207 " mu:=596; f2:=statevalf[icdf,normald[0,1 ]]:\n\nn:=400: p:=0.025: # P(X<=n)<=p \n # Hersteller behauptetz. B. , dass h\366chstens p=2,5% der Birnen k\374rzer als n=400 Stunden halt en.\n k:=f2(p);# kleinergleich \n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#muG\"$'f" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"kG$!+&)R'*f>!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "# mittlere Lebensdauer mu ss mindestens sein:\n solve( (n-mu)/s=k,s); # gr\366\337ergleich, au frunden" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+v$=++\"!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "\n# zSigma-Umgebung" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 210 "restart:\nwith(stats): with(statev alf):\nf1:=statevalf[cdf,normald[0,1]]:\nf2:=statevalf[icdf,normald[0, 1]]:\nn:=50: p:=22/50.; alpha:=0.90:\nmu:=n*p;\nsigma:=sqrt(n*p*(1-p)) ;\nz:=f2((1-alpha)/2);\nz:=f2((1+alpha)/2);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG$\"+++++W!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#muG$\"+++++A!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG$\"+bd) *4N!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG$!+FO&[k\"!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG$\"+FO&[k\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "linkeGrenze:=mu-z*sigma;\nrechteGre nze:=mu+z*sigma;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,linkeGrenzeG$\" +?(eEi\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-rechteGrenzeG$\"+!G Ttx#!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "# Konfidenzintervall N\344herung \+ \n n:=50: X:=22: p:=X/50.; alpha:=0.90:\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG$\"+++++W!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "mu:=n*p;\nsigma:=sqrt(n*p*(1-p));\nz:=f2((1+alpha)/2 );\nz:=-f2((1-alpha)/2);\n\np_max:=solve(X/n=p1-z*sigma/n,p1);\np_min: =solve(X/n=p2+z*sigma/n,p2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG $\"+++++A!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG$\"+bd)*4N! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG$\"+FO&[k\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG$\"+FO&[k\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&p_maxG$\"+gDoab!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%&p_minG$\"+SuJXK!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "# Konfidenzintervall ex akter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "fsolve(X=n*pmax-z* sqrt(n*pmax*(1-pmax)),pmax);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Xp (eb&!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "fsolve(X=n*pmin+ z*sqrt(n*pmin*(1-pmin)),pmin);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+xGs0L!#5" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart;\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(stats): with(statevalf):" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "# Aufgabe Stan dardabweichung sigma und Erwartungswert mu sind gesucht,\n# zwei Wahrscheinlichkeiten sind gegeben" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 " f2:=statevalf[icdf,normald[0,1]]:\n\nn1:=22: p1:=0. 60: # P(X<=n1)<=p1 \nn2:=18: p2:=0.10: # P(X<=n2)<=p2\n\ngl1:=(n1- mu)/sigma=f2(p1);\ngl2:=(n2-mu)/sigma=f2(p2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl1G/*&,&\"#A\"\"\"%#muG!\"\"F)%&sigmaGF+$\"+J5ZLD!# 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$gl2G/*&,&\"#=\"\"\"%#muG!\"\"F )%&sigmaGF+$!+m:b\"G\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "\n solve(\{gl1, gl2\}, \{mu,sigma\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%&sigmaG$\"+E_.1E!\"*/%#muG$\"+_o(R8#!\")" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 245 "restart:\nwith(stats): with(statevalf):\nf2:=statevalf[icdf,nor mald[0,1]]:\nalpha:=0.90:\nd:=0.05: # L\344nge des Vertrauensintervall s\nz:=f2((1+alpha)/2);\nz:=evalf(z,3); # gerundet \np:=0.2:# oder Sch \344tzung verwenden \nsigma:=sqrt(n*p*(1-p));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "fsolve(2*z*sigma/n=d,n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG$\"+FO&[k\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%&sigmaG,$*&$\"+++++S!#5\"\"\"%\"nG#F*\"\"#F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Z7>Ep!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }