f(z)= \frac{1}{\sqrt{2π} } e^{-\frac{z ^2}{2}} \ \ \ (-\infty < z< \infty)

$m$

\frac{1}{\sqrt{2π}}

\mathrm{O}

y

z

2

3

4

5

1

6

\mathrm{N}(0,1^2)

$a$

8

$\mathrm{P}(a \le \mathrm{X} \le b)$

9

10

11

7

z=

\mathrm{P}(0 \le \mathrm{Z} \le z) 

$a$

$\mathrm{P}(a \le \mathrm{X} \le b)$

\mathrm{P}(\mathrm{Z} \ge z \ge0) 

k = 1
E: (4.827735836033162, 0)
σ = 1 (slider from 0 to 10)
m = 0 (slider from -5 to 5)
f(x) = (1 / ((sqrt((2 * π)) * σ)) * ℯ^(((-(x - m)^(2))) / ((2 * σ^(2)))))
g: x = m
A = Intersect(f, g, (0, 0.3989422804014327))
B = Point(g)
h = Segment(B, A)
i = Line(A, xAxis)
b = true
c = true
d = true
e = true
D: ((-x(E)), 0)
u = Vector(D, E)
F: (0, -0.3)
G: (0, 2.466287047793652)
v = Vector(F, G)
a = true
o = true
I: (k, 0)
H: (0, 0)
p = true
q = Integral(f, x(H), x(I))
J: (x(H), f(x(H)))
K: (x(I), f(x(I)))
r = Segment(H, J)
s = Segment(I, K)
t = Segment(H, I)
w = true
a_1 = true
b_1 = true
d_1 = true
텍스트6: "" + (x(I)) + ""
텍스트5_1: "=" + (LaTeX[q]) + ""
입력상자1 = Textfield(k)
I_1: (k, 0)
텍스트6_1: "" + (x(I_1)) + ""
입력상자1_1 = Textfield(k)
텍스트5: "=\mathrm{P}(0 \le \mathrm{Z} \le " + (LaTeX[x(I)]) + ") "
f_1(x) = (1 / ((sqrt((2 * π)) * σ)) * ℯ^(((-(x - m)^(2))) / ((2 * σ^(2)))))
g_1: x = m
I_2: (k, 0)
H_1 = (2.196815030216288, -0.013312426003288191)
q_1 = Integral(f_1, x(H_1), x(I_2))
J_1: (x(H_1), f_1(x(H_1)))
K_1: (x(I_2), f_1(x(I_2)))
t_1 = Segment(H_1, I_2)
텍스트6_2: "" + (x(I_2)) + ""
입력상자1_2 = Textfield(k)
I_3: (k, 0)
입력상자1_3 = Textfield(k)
텍스트5_5: "=" + (LaTeX[0.5 - q]) + ""
텍스트5_4: "=\mathrm{P}( \mathrm{Z} \ge " + (LaTeX[x(I_2)]) + "\ge 0) "