SQL & PL/SQL

Hi,
I am trying to achieve allowing regular Users to perform limited table operations on table's present in another schema.
For that I have created a procedure to analyze any table in the SYSTEM schema.
I have table EMP in the SCOTT schema.
I have different database users say User1, User2 etc.
User1 , User2 are the regular users who has just read access on SCOTT.EMP table.
I want to give them the ability to analyze the SCOTT.EMP table using the Procedure compiled in the System schema.

So I created the following procedure in the SYSTEM Schema and granted the execution privilege to Public.

----------------------------------------------------------------------------------------------
SYSTEM>

CREATE OR REPLACE PROCEDURE analyze_any_table(i_Owner varchar2, i_Table varchar2)
AS
BEGIN
DBMS_STATS.GATHER_TABLE_STATS(
ownname => i_Owner
,tabname => i_Table);
END;
/

GRANT EXECUTE ON analyze_emp TO PUBLIC;
----------------------------------------------------------------------------------------------

Now I logged in as the USER1

USER1> EXEC SYSTEM.analyze_emp;

ERROR at line 1:
ORA-20000: Unable to analyze TABLE "SCOTT"."EMP", insufficient
privileges or does not exist
ORA-06512: at "SYS.DBMS_STATS", line 13046
ORA-06512: at "SYS.DBMS_STATS", line 13076
ORA-06512: at "SYSTEM.ANALYZE_ANY_TABLE", line 3
ORA-06512: at line 1

How to get out of this error.
I don't want to give "GRANT ALL ON SCOTT.EMP TO PUBLIC" to any other database users.

Note: if I compile the above procedure in the SCOTT schema it works. But I don't want to duplicate this analyze_any_schema procedure in multiple schema's which has some table.

Any suggestion would be really appreciated.
Thanks
Balaji