using expdp backup database

You need to grant read and write permission on directory to user for taking backup.(Assuming that you have all the rights)

GRANT read, write ON DIRECTORY data_pump_dir TO scott;

What the error message is telling you, is that the user SCOTT does not have the privileges to write to DATA_PUMP_DIR.

As the DBA run

grant read, write on directory DATA_PUMP_DIR to scott;

Is D:\app\Administrator\admin\orcl\dpdump\ a directory on the server? It has to be accessible from the Oracle server software to be valid, as the export actually runs on the server and not the client.