Run the Norton Removal Tool: http://service1.symantec.com/Support/tsgeninfo.nsf/docid/2005033108162039
Sorry I'm not really sure if it works on a Mac.
The jucheck is the Java Update Checker and it is advisable to let it run. But although I'm not au fait with a Mac you should be able to adjust update settings in the Control Panel/Additional Options or Classical View > Java in Windows, whatever the equivalent is in a Mac.
Thanks for the response. You are my hero for the day. I feel pretty dumb if jucheck.exe is a good thing. I thought from my reading that it was anything from a worm to a Trojan. I am confused. Can I assume that some bad things simply use jucheck.exe to gain entry and then cause havoc? I suspect I should just let it load, and assume if something bad is potentially going to happen, McAfee will find it most likely. Am I right? The new lap top is Windows 7 by the way, and it is taking some getting use to.
I suppose it could be vulnerable - that's why it's always wise to keep an extra one or two anti-spyware tools handy just in case. That and always keep everything up to date.