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First off, the OT - topic.
That works out to be ~87.7 people per sq km - had to convert - sorry, everyone uses km these days! 
That means you had a comparable pop density to Dominica or Turkey, which are 107th and 108th on the world ranking (1999 figures). Source is here. The US is 172nd out of 239 states and island territories on this list, so not much of a good comparison really.
Secondly, the On Topic bit.
Using the Civ Calculator, an Elite Longbowman in those circumstances had a 7.5% chance of winning. Of course the exact odds depend on the exact strength of your Infantry that each Longbowman faced, but assuming (as an upper limit on their chances) your Infantry was reduced to 1 hp first time, then promoted, then promoted again at 1hp left, then defended the rest of the 25 LBs at 1hp left, the chances of your victory were = about 8.3 x 10^-6 %.
If your Infantry defended with no hp loss at all the whole time to Regular Longbowmen (an upper limit on YOUR chances), the chances were = 94.5%. Thus there was a very good chance of you achieving this outcome, especially since the most probable outcome each time was for your Infantry to win with no hp loss.
No apologies for not doing the stats fully - this will do, and if you ARE offended by the crudeness of these estimates, why are you wanting to do the stats exactly anyway?
I just did a quick calculation on the population and land area. It seems that I have 224.5 people per square mile. That's quite a number considering what the average is for the USA.
That means you had a comparable pop density to Dominica or Turkey, which are 107th and 108th on the world ranking (1999 figures). Source is here. The US is 172nd out of 239 states and island territories on this list, so not much of a good comparison really.
Secondly, the On Topic bit.
Using the Civ Calculator, an Elite Longbowman in those circumstances had a 7.5% chance of winning. Of course the exact odds depend on the exact strength of your Infantry that each Longbowman faced, but assuming (as an upper limit on their chances) your Infantry was reduced to 1 hp first time, then promoted, then promoted again at 1hp left, then defended the rest of the 25 LBs at 1hp left, the chances of your victory were = about 8.3 x 10^-6 %.
If your Infantry defended with no hp loss at all the whole time to Regular Longbowmen (an upper limit on YOUR chances), the chances were = 94.5%. Thus there was a very good chance of you achieving this outcome, especially since the most probable outcome each time was for your Infantry to win with no hp loss.
No apologies for not doing the stats fully - this will do, and if you ARE offended by the crudeness of these estimates, why are you wanting to do the stats exactly anyway?
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