Correct me if I'm wrong, but the basic calculation gives you the current out of the Arduino pin. Assuming a 0.7V drop over the base/emitter junction you have:
(5 - 0.7) / 2200 = 0.0019 A
So you are letting around 2 mA flow, which is well within spec for the output pin. One of the pages linked above suggested 1k, which would give:
(5 - 0.7) / 1000 = 0.0043 A
Still within spec for the pin.
Presumably that is enough to turn on the transistor (isn't it voltage that turns it on rather than current?).