Most of "those" kids who don't make it close to applying are the ones who, freshman year, thought that being a doctor like on House and making a lot of money would be cool. Then, after joining a greek organization and failing their first test, they switched to something else.
Edit: So you shouldn't compare OPs chances of becoming a doctor to an overall statistic.
A good doctor isn't someone who buries their head into a book and studies 24/7. A good doctor is someone who manages time well, studies when they need to, is reasonably intelligent, and has an innate curiosity about medicine and the body.