Tom,
Once you've published your content with the quiz in the
Content Library, you will need to create a Training Course with
that content and set enrollment of users. Yes, they will need to be
fully qualified users with Connect. to track the answers in the
manner you're looking for. If you don't have the "Training" tab in
your account, you won' t be able to perform this function. If you
are taking about a lot of people taking the quiz, I suggest you use
the Events Module for self enrollment, where you can then make them
users to Connect more easily.
Feel free to PM me if you need more help.