The good news is that every student who applies is considered for the Murray Scholarship. We identify 50-70 applicants who we want to compete for the scholarship and they are notified in January/February and asked to write an additional essay. From there, we cut to a pool of 20 finalists who are invited to campus for a weekend in April as the final stage of the selection process.
However, only four students a year are awarded the scholarship and we have an applicant pool of over 12,000 so the odds are against any student. We award the Murray to the best of the best in our applicant pool and best of the best in every sense (grades, curriculum, testing, extracurriculars and accomplishments, etc).
There's no way to know if your student will receive the scholarship unless an application is submitted and that only costs the $60. application fee and the time completing the app (and given we use the Common App hopefully that can go to several schools on your student's list).