I'm experienced when coming to Pokemon so I'll try my best to help you. Norman has three pokemon which are 2 Slaking's and one Vigoroth.
Slaking: Lv. 28
Vigoroth: Lv. 30
Slaking: Lv. 31
Since Norman is a Normal type Gym Leader your best bet are Fighting type since they are weak against them. Now, if you don't have a Fighting type then you might have some what of a hard time against him since all three of his Pokemon know the move Facade which can pretty much do some serious damage if your not careful. So you will need a lot of potions and revives to keep yourself in the battle.
But other them the move Facade he will be pretty easy to beat if you have the right Pokemon or if you play your cards correctly. His first Slaking as we all know due to it's name Slack's off giving you another chance to hit him, this make's it easier to beat him.
His second Pokemon Vigoroth to me was probably the most annoying to beat since he has the moves Slash and Facade. From my experience you should try to put him to sleep to keep him from attacking you. Or you could confuse or poison him. This make's it faster to beat him.
Now his last Slaking is probably the easiest of them all considering he has the move Focus Punch after a few turns. Which gives you the upper hand, if you see he's getting ready to use Focus Punch then hit him hard and he won't be able to move since he lost focus. Keep doing that and you'll beat him in no time at all.
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Beat the Gym Leader
Try his perents house
The eighth gym leader is in the underwater city(forget the name) but it is where you fight groudon. after you beat him the gym should be open.
Train he isn't very good
In the 8th gym. he is the gym leader