the tire was installed backwards (arrow pointing backwards) how much would it cost if i took it off the bike myself and brought it to a bike shop to correct it?
If it's the front tire, you'll probably never have any problem unless you're doing stoppies all the time. If on the rear of a small, low power bike, that'll probably never cause any problem either. If on the rear of a high horsepower machine and you like to smoke the tire or race, then you better get it changed.
Most places charge $20-$30 to mount a tire (off the bike). Used bike?
Most shops I go to charge $25 if the wheel is still on the bike and $20 if it's off. Edit: You don't want to do it yourself. if you ding the rim the wrong way, you'll cost yourself more.