Moonstruck...What %-age of the time is the moon visible during daylight hours vs. nighttime hours?

As I was driving home this afternoon with daughter from upstate New York, the gibbous moon was the exact same shade of off-white as the bank of clouds nearby. At first it looked like a large piece of a large cloud had broken free and was setting sail in another direction. I was "moonstruck", but it was only 3pm or so. So I started wondering: during the 365 days of the year, is the moon visible in the sky during the daytime the same amount of time that it is visible in the sky after sundown? Astronomy whizzes out there, you know?