It is very much a factor of where you apply. If you apply to a range of schools, including a few where your scores are well above the average admit, you will have a good chance. It is, however, hard to define since so many apply to only the top 5 schools. The most active posters on this board do not often discuss the top 50 schools. It is hard to know how broad an applicant list was. As has been said MANY times before, if your goal is to go to boarding school (ANY boarding school), then you need to have a varied list. If you have a good option at home then, by all means, feel free to limit yourself to the top 5. Every year there are kids who are shocked to find that they were rejected from all schools. Do your research, be open-minded and you might have good news.