According to FermiLab, you're off by a factor of about 1,000...
From FermiLab:
Our universe is permeated with neutrinos nearly massless, neutral particles that interact so rarely with other matter that trillions of them pass through our bodies each second without leaving a trace. These tiny particles, studied in world-leading Fermilab experiments, could be key to a deeper understanding of our universe.
http://www.fnal.gov/pub/science/particle-physics/experiments/neutrinos.html
Fermilab is managed by Fermi Research Alliance for the U.S. Department of Energy Office of Science. FRA is a partnership of the University of Chicago and Universities Research Association, Inc., a consortium of 89 research universities.
Oops! Sorry. FermiLab of course actually said trillions pass through our *entire bodies*, not just square centimeter, or square inch.
I said *per square centimeter*. Add all those up and I'm pretty close again.