How many professors are there?
select count ( * ) from professor
How many have a Ph.D. degree?
select count ( * ) from professor where prof_high_degree = "Ph.d."
Yes
select t2.dept_name from professor as t1 join department as t2 on t1.dept_code = t2.dept_code where t1.prof_high_degree = 'Ph.d.' group by t1.dept_code order by count ( * ) desc limit 1