Question

X is normally distributed with mean 12 and SD 4. Find P(X ≤ 20) and P(0 ≤ X ≤ 12)

Answer 1

X is normally distribution with mean 12 and SD 4

∴ µ = 12 and σ = 4

Standard normal variable

z = `(x - mu)/sigma`

= `(x - 12)/4`

P(X ≤ 20)

When x = 20

z = `(20 - 12)/4 = 8/4` = 2

v(x ≤ 20) = `8/4` = 2

P(x ≤ 20) = P(z ≤ 2)

= 0.5 + p(0 < z < 2)

= 0.5 + 0.4772

= 0.9772

P(0 ≤ X ≤ 12)

When x = 0

z = `(0 - 12)/4 = (-12)/4 = - 3`

When x = 12

z = `(12 - 12)/4 = 0/4` = 0

P(0 ≤ x ≤ 12) = P(-3 ≤ z ≤ 0)

= P(0 ≤ z ≤ 3)

= 0.4987