Parents need to consider many factors for pre-med student - GPA, MCAT and undergrad selectivity. It is not an easy path for premed and possibility of getting into med school differs between elite private and public state flagship. Check the following article about the impact of med school admission from elite private vs public based on real data.
https://www.collegetransitions.com/blog/from-pre-med-to-md-understanding-the-pathways-to-medical-school/
