Other Properties of the Normal Distribution:

• If X is a normal random variable and a and b are constants, then Y = aX + b will have a normal distribution as well.

In fact, if X ~ N(μ, σ), then Y ~ N(aμ + b, |a|σ).

• If X and Y are independent random variables who each have a normal distribution then X + Y and X – Y also have a normal distribution.