There should be no expectation at all that a new rifle will be properly zeroed. Any AK owner should have a front sight tool. My instructions for zeroing can be found here (scroll to bottom of page):
http://www.ultimak.com/AKST.htm
Your group size is a separate issue. Unless the front or rear sight is loose and flopping around, you should be getting 2 inches at 50 and more like 4 or 5 at 100. Some AKs can do substantially better than that, approaching 1 MOA.
If you are first starting out on rifle shooting, your stated group size is fairly normal, no matter the particular weapon. Breathing, consistency of hold from shot to shot, trigger control, sight picture, and the big one - flinch avoidance, if all brought together at the moment of release, and all held consistent from shot to shot, will tighten your groups considerably. Also, a hot barrel will shoot to a different point of impact, and with a larger group, than a cold barrel. If you really want to know what you and your rifle can do, shoot with a relatively cool barrel.
You can practice flinch avoidance by dry firing after firing several live rounds. You will be astonished at how much you flinch without ever realizing it. You should not even blink. Practice that. I know guys who record themselves on video so they can see their faces while shooting. Feedback of this kind can be highly instructive.
Rifle marksmanship is often more of a mental process than a physical one.