Do NOT install Norton on your Mac.
There are many forms of ‘Malware’ that can affect a computer system, of which ‘a virus’ is but one type, ‘trojans’ another. Using the strict definition of a computer virus, no viruses that can attack OS X have so far been detected 'in the wild', i.e. in anything other than laboratory conditions. The same is not true of other forms of malware, such as Trojans. Whilst it is a fairly safe bet that your Mac has NOT been infected by a virus, it may have another security-related problem, but more likely a technical problem unrelated to any malware threat.
You may find this User Tip on Viruses, Trojan Detection and Removal, as well as general Internet Security and Privacy, useful:
The User Tip (which you are welcome to print out and retain for future reference) seeks to offer guidance on the main security threats and how to avoid them.
More useful information can also be found here:
OS X already includes all the anti-virus protection it needs to protect itself from viruses and malware. You do not need to buy anything else.
Nearly all third party Mac anti-virus utilities are junk. Most are worthless, some are harmful, none are necessary.
Windows viruses have no affect on OS X, but they can be carried in emails sent to you. If you want to detect and / or eradicate Windows viruses from your Mac, use ClamXav. It is in the App Store and it is free.
I am a XPC user and have Norton on that machine.
While Norton / Symantec is generally recommended for PCs, it is one of the worst examples of such junk. Do not install it.