The Normal Distribution

Showing the relationship between a given normal distribution and the standard normal distribution

a =

b =

a =

a =

\mathrm{Standard \ Normal} \ Z  \sim N(0,1)

\text{Normal with mean} \ \mu \ \text{and variance} \ \sigma^2, \text{i.e} \ X \sim N(\mu,\sigma^2)

mu = 2.4 (slider from -5 to 5, step 0.05)
sigma = 0.3 (slider from 0 to 4, step 0.05)
f(x) = (1 / ((sigma * sqrt((2 * π)))) * exp(((-(x - mu)^(2))) / ((2 * sigma^(2)))))
g(x) = (1 / sqrt((2 * π)) * ℯ^(((-x^(2))) / 2))
a = 1.2
b = 2.4
InputBox1 = Textfield(a)
InputBox2 = Textfield(b)
intval = Integral(f, a, b)
z1: (a - mu) / sigma
z2: (b - mu) / sigma
normintval = Integral(g, z1, z2)
text1: "P(a \leq x \leq b) = " + (LaTeX[intval]) + ""
InputBox1_1 = Textfield(a)
z1_1: (a - mu) / sigma
text2_1: "z_1 = \frac{a-\mu}{\sigma} = " + (LaTeX[z1_1]) + ""
InputBox1_2 = Textfield(a)
z1_2: (a - mu) / sigma
text2: "z_2 = \frac{a-\mu}{\sigma} = " + (LaTeX[z2]) + ""
text3: "P(z_1 \leq x \leq z_2) = " + (LaTeX[normintval]) + ""