Yes it depends on where you set the threshold. If you try to keep as close to your academic standards as possible, but also admit some kids from the bottom 25%

Yes it depends on where you set the threshold. If you try to keep as close to your academic standards as possible, but also admit some kids from the bottom 25% of income then you'll get mostly Asians. If you set a much lower threshold and do a lottery as you propose it depends much more on the composition of the applicant pool.