RE: Is this normal?
If I were you, before I got too upset or carried away, I'd change that scope. At the very least, make sure the rings and bases are tight.
Also, when shooting for groups, clean the rifle between each 3 shot group and let the barrel complete cool. That way each ammo brand is starting off the same as the others. It wouldn't surprise me that you'll see marked improvements in your shooting.
I respect, but disagree with Nomercy about one thing. I believe that most rifles now days, with the right shooter and ammo, will consistantly shoot better than 2". Some a lot better.