μ

\mathscr{C}_f

μ-σ

μ+σ

k = 1 (slider from 1 to 3, step 1)
σ = 1 (slider from 0.1 to 5, step 0.1)
kσ: (k * σ)
μ = 0 (slider from -10 to 20, step 0.1)
borne_{sup}: μ + kσ
borne_{inf}: μ - kσ
f(x) = (1 / ((σ * sqrt((2 * π)))) * exp((-1 / 2 * ((x - μ) / σ)^(2))))
A: (μ, 0)
A': (x(A), f(x(A)))
B: (((2 * μ) + σ) / 2, f(((2 * μ) + σ) / 2))
texte3: "X \; est \; une \; variable \; aléatoire \; qui \; suit \; la \; loi \; \mathscr{N} \left(" + (LaTeX[μ]) + " ; " + (LaTeX[σ]) + "^2 \right )"
a = Integral(f, μ - (k * σ), μ + (k * σ))
A'': (A + A') / 2
texte4: "" + (LaTeX[a]) + ""
D_1: (borne_{inf}, -0.04)
D_2: (borne_{sup}, -0.04)
u = Vector(D_1, D_2)
v = Vector(D_2, D_1)
texte10: "μ-" + (LaTeX[k]) + "σ"
texte11: "μ+" + (LaTeX[k]) + "σ"
E: (x(A'') - (0.9 * σ), y(A'') - 0.02)
F: (x(A'') - (0.9 * σ), y(A'') + 0.02)
G: (x(A'') + (0.9 * σ), y(A'') + 0.02)
H: (x(A'') + (0.9 * σ), y(A'') - 0.02)
poly1, f_1, e_1, h_1, g = Polygon(F, E, H, G)
C_1: (borne_{inf}, 0)
C_2: (borne_{sup}, 0)
texte6: "p \left( \mu-\sigma \; ≤ \; X \; ≤ \; \mu+\sigma \right) \; = \; p \left( " + (LaTeX[borne_{inf}]) + " \; ≤ \; X \; ≤ \; " + (LaTeX[borne_{sup}]) + " \right) \; ≈ \; " + (LaTeX[a]) + ""
texte5: "p \left( \mu-" + (LaTeX[k]) + "\sigma \; ≤ \; X \; ≤ \; \mu+" + (LaTeX[k]) + "\sigma \right) \; = \; p \left(" + (LaTeX[borne_{inf}]) + "   \; ≤ \; X \; ≤ \; " + (LaTeX[borne_{sup}]) + "  \right) \; ≈ \;  " + (LaTeX[a]) + ""