Well, your question is interesting because it's hard to say what an "average" shooter is plus a .380 is not a first or even second choice to reach out and touch something at 15 yds.
That said, my SWAG would be that most anyone who has practiced the basics (good grip, focus on front sight and smooth trigger press keeping the rest of the hands steady) should be able to consistently hit a sheet of copy paper or better at 15 yds. A "better than average" shooter would do better.