It's common knowledge that minorities and poor people are charged more often and face stiffer sentences. I'm feeling lazy, too, but if someone doubts me, holla, and I'll post some links.
The thing is, it's hard to tell how much of it is being colored and how much of it is being poor, as the two overlap more significantly than white and broke, statistically speaking. Rich white will get a better sentence than poor white. Poor white will get a better sentence than poor black. Middle class white will get a better sentence than middle class black, but the disparity is less severe than poor white vs. poor black. Rich white and rich black enjoy relatively equivalent sentencing, because money is the great equalizer.
White privilege is real, but so is socioeconomic privilege. Juries will have a harder time sympathizing because she's black. But, if she doesn't have something like an existing diagnosis on record which will help the defense, that's not because she's black, it's because she's poor. But being black does make it easier to be poor.
Chicken and the egg, much?
It's a fucking mess. But, yeah, an insanity defense is hard to get to begin with. Even harder when you're black.