Is it possible for a DBA to grant execute to a user via user defined roles for functions and packages that the DBA created and owns?

Also, can a DBA that has been granted execute on an Oracle restricted package (such as utl_file or dbms_random) be able to create a role, grant execute to one of the packages mentioned to that role and then grant that role to another user. Would that user then be able to use utl_file or dbms_random?

Of course, it is noted that sys has revoked execute from public for those two packages (utl_file and dbms_random).