Here is an excerpt from the Class of 2012 Profile, similar to the one referenced.
USNA Class of 2012 Academic Profile
SAT (ACT) Program Scores
Verbal
700-800 (31-36).........26%
600-699 (26-30).........43.8%
<600 (<26)................29.9%
Math
700-800 (31-36).........32.7%
600-699 (26-30).........49.2%
<600 (<26)................18.1%
Rank in High School Class
Top 20%...................76.0%
Top 40%...................15.0%
Middle 20%................8.0%
Lower 40%.................1.0%
Bottom 20%................< .1%
The USNA Admission Board does not have a 'minimum' SAT/ACT or GPA requirement. USNA selects candidates based upon a whole-person assessment and look for a combination of strengths in academics, athletics and leadership. That being said, these figures give candidates an indication of the academic caliber the Board can choose from when filling a class. If a candidate wants to be competitive for a USNA appointment, SAT/ACT scores should be well into or above the 600s/high 20s. Additionally, a candidate should be well placed in the Top 40th-percentile of his/her high school graduating class.
If you do the math in reverse, candidates with SAT/ACT scores under 600/26 have about a 20% chance of being offered appointment. Similarly, a candidate has even less of a chance (~10%) if not in the top half of their high school graduating class.
Best of luck and BEAT ARMY!