I'm running my site on a dedicated server since sevaral weeks now and now found out with portsentry/logcheck that the server gets about 3 portscans per day. My site has about 1000 visitors per day.
Is this a normal percantage or is this a very high number?

Probably not!!

Nowadays people are portscanning all the time (script kiddies) looking very well known exploits hoping the will get lucky. As long as your box is up to date I would not worry very much about it!! :D :D

as RFhost already said ...
that's pretty normal. and three isn't that much.
i receive much more than that. portscans, anonymous ftp login attempts, ppl scanning for iis wholes and so on. pretty funny sometimes =)
so just keep your stuff upd 2 date ... and you'll be fine.