Is this amount of guitar hum normal?

You probably just need to move away from your computer, and maybe mess around with the angle you face the computer.
 
I would say its more than normal. There are some reasons which creates this kind of noise. Its possible that you don't have a proper grounding in your house, in your room or the plug you use. Maybe your computer's monitor (if its a CRT one) is facing to your guitar in such an angle that it creates noise. Also it can be the flauroscent lightning if you are using one. You should check your guitar's cable too to see if it travels over, or paralel to one of your power cables. If you are using a notebook to record, try unplugging the battery charger to see if it removes the hum. Sony's notebooks creates so much hum and the only way to overcome is unfortunately unplugging the charger and recording with the battery.