What kind of administrative duties might a postdoctoral associate be expected to take on?
I think you need to find out exactly what they are expecting from you.  I would normally associate postdoc positions with research duties rather than administrative duties.  Some exceptions that I have known involve postdocs who are expected to act as the supervisor for a number of graduate or undergraduate researchers, but these are unusual cases.  Contact the people offering the position, and find out what exactly the administrative duties mean: otherwise, you won't know how to tailor your application, and (more importantly) you might end up in a position you really didn't want!