In a solution I am trying to understand, we are given:

$\displaystyle A \sim N(\mu, 0.04)$

$\displaystyle B \sim N(\mu, 0.04)$

And then the next step is written as:

$\displaystyle (\bar{A}-\bar{B}) \sim N(0, 0.08)$

Can someone please explain to me how this step is made? I can see why the mean would be zero, but why are the variances summed? Thank you.