K:\EKV\PBM_BBS\40_GYV_Projekte\10_Lambacher_Schweizer\P048_15850_LS_SII_NW_22\735481_LS_Qualiphase_LK_SB\03_Beilagen\01_Red\04_Medien\Kap_10 Assets\fertig bearbeitete von Anna\Sigmaregeln

P(X=a)

P(X≤a)

P(X≥b)

P(a≤X≤b)

cσ-Umgebung

Graph zu P(X≤x)

Graph zu P(X≥x)

n = 80 (slider from 0 to 400, step 1)
p = 0.22 (slider from 0 to 1, step 0.01)
L_1 = Sequence(BinomialDist[n, p, k, false], k, 0, n)
L_2 = Sequence(0, n)
Breite = 0.6 (slider from 0 to 1, step 0.1)
BDiagramm = BarChart(L_2, L_1, Breite)
σ: sqrt(((n * p) * (1 - p)))
μ: (n * p)
a = 10 (slider from 0 to n, step 1)
b = 13 (slider from a to n, step 1)
c_{1} = false
L_3 = Sequence(0, a)
L_4 = Sequence(BinomialDist[n, p, k, false], k, 0, a)
d = BarChart(L_3, L_4, Breite)
e = false
Pkgk = BinomialDist(n, p, a, true)
Pgleichk = BinomialDist(n, p, a, false)
Pggk: 1 - BinomialDist[n, p, b - 1, true]
L_5 = Sequence(b, n)
L_6 = Sequence(BinomialDist[n, p, k, false], k, b, n)
f = BarChart(L_5, L_6, Breite)
g = false
L_7 = Sequence(a, b)
L_8 = Sequence(BinomialDist[n, p, k, false], k, a, b)
h = BarChart(L_7, L_8, Breite)
Pvonbis: BinomialDist[n, p, b, true] - BinomialDist[n, p, a - 1, true]
j = false
c = 2 (slider from 0 to 5, step 0.01)
rechts: μ + (c * σ)
links: μ - (c * σ)
li: ceil(links)
re: floor(rechts)
wert: BinomialDist[n, p, re, true] - BinomialDist[n, p, li - 1, true]
li0: floor(links)
re0: ceil(rechts)
wert0: BinomialDist[n, p, re0, true] - BinomialDist[n, p, li0 - 1, true]
i = true
l = Segment((links, 0), (rechts, 0))
L_9 = Sequence(li, re)
L_{10} = Sequence(BinomialDist[n, p, k, false], k, li, re)
m = BarChart(L_9, L_{10}, Breite)
L_{11} = Sequence((k, BinomialDist[n, p, k, true]), k, 0, n)
q = PolyLine(L_{11})
o = false
L_{12} = Sequence((k, 1 - BinomialDist[n, p, k - 1, true]), k, 0, n)
r = PolyLine(L_{12})
s = false
Text6: "" + (LaTeX[If[c_{1} ≟ true, "P(X=" + a + ")=" + Pgleichk] + "\\"]) + "" + (LaTeX[If[e ≟ true, "P(X≤" + a + ")=" + Pkgk] + "\\"]) + "" + (LaTeX[If[g ≟ true, "P(X≥" + b + ")=" + Pggk] + "\\"]) + "" + (LaTeX[If[j ≟ true, "P(" + a + "≤X≤" + b + ")=" + Pvonbis]]) + ""
BDiagrammrot = BarChart({a}, {BinomialDist[n, p, a, false]}, Breite)
Text1: "μ=E(X)=n\cdot p\, ; \quad μ=" + (LaTeX[n]) + "\cdot " + (LaTeX[p]) + "=" + (LaTeX[μ]) + "\\
σ=\sqrt{n\cdot p\cdot (1-p)}\, ; \quad σ=\sqrt{" + (LaTeX[n]) + "\cdot " + (LaTeX[p]) + "\cdot" + (LaTeX[1 - p]) + " }=" + (LaTeX[σ]) + ""
γ: (2 * Normal[0, 1, c, true]) - 1
fehler: ((wert - γ) / γ * 100)
Text2: "σ=" + (LaTeX[σ]) + ",  \text{Sicherheitswahrscheinlichkeit } P=" + (LaTeX[round((γ * 100), 2)]) + "\,%\\" + (LaTeX[c]) + "\!\cdot\!σ\text{-Umgebung von }μ=" + (LaTeX[μ]) + "\!:\quad [" + (LaTeX[links]) + "; " + (LaTeX[rechts]) + "]\\
P(" + (LaTeX[li]) + "≤X≤" + (LaTeX[re]) + ")=" + (LaTeX[wert]) + ";\quad Abweichung: " + (LaTeX[fehler]) + "%"