It's not normal
I have flown the Archer II a lot (same engine) and I usually saw 2400 rpm at full power runup (2300 at least). 2200 is totally unaceptable. Even at a high hot field, I think the rpm would be the same, as the propeller drag decreases at a rate close to engine power loss.
The mixture may be too rich (more likely) or too poor.
In flight, I have always retarded the throttle to avoid exceding 2500 rpm. Your plane is definitely out of shape.