http://datacenter.kidscount.org/data...gs.aspx?ind=99
This site has the breakdown of "under 18 year olds" by state. Low: 21% in Maine (19% in DC). High: 31% in Utah.
That's a 50% difference in that demographic by percentage, so I think it is worth taking into account.
(Granted, this number represents age 0 - 18, and I don't know a lot of newborns who are participating in FIRST. But in 5 years they could be in Jr. Lego League).
EDIT:
Here is a better set of numbers that has a finer breakdown by state. But you'd need to compute percentages yourself.
EDIT 2: I did the math. US average for 14-17 year olds (the majority of FRC participants - unfortunately 18 year olds were in the next bin) is 5.72% of population. Maximum: 7.30% in Utah. Minimum: 5.11% in Massachusetts (3.94% in DC).