H2 Maths 6.3 - Normal Distribution: Linear Combinations

What you will learn

• If X and Y are independent normals, a X + b Y is normal with mean a mu_X + b mu_Y and variance a^2 sigma_X^2 + b^2 sigma_Y^2.
• X ~ N(40, 16) and Y ~ N(60, 9) independent: X + Y ~ N(100, 25).
• P(X + Y > 108): Z = (108 - 100) / 5 = 1.6; P(Z > 1.6) about 0.0548.