How long does it take to become good at piano?

I'm a beginner. I just started learning in Feb 2010 with a teacher. We are working with the "John Thompson's Modern Course For The Piano." I recently started the third grade book. I want to know how long it takes to have dexterity with the fingers. I know everyone is different, but say the avg. person? My goal later on is to be able to play Chopin Nocturnes, Preludes, and Etudes. And some Beethoven and Tchaikovsky. But i don't know how long that takes. &&& I'm 19 years old and i practice atleast 2 1/2 hrs. per day. I use some Hanon and Czerny exercises. And I learned the major scales with up to six sharps and only 2 flats (still learning the others). Also during my spare time, i do some music theory - currently on intermediate theory.