Hi all can you help?

I have recently downloaded the zonealarm free program.My internet connection is tethered through my mobile phone to my pc.Having recently had Mcafee security installed i had noticed i was getting around 50-60 incoming network attempts per day.First question,is this normal? and why? 2nd question after installing zonealarm i am not recieving anything in the log about any kind of activity? is this normal?

Any help would be much appreciated

Many thanks