Question

A random variable X ~ N (0, 1). Find P(X > 0) and P(X < 0).

Answer 1

Given X ∼ N(0, 1)

∴ μ = 0

∴ P(X > μ) = P(X > 0) = `1/2` as the distribution is symmetric about μ = 0.

P(X < μ ) = P(X < 0) = `1/2` as the distribution is symmetric about μ = 0.