Windows Update doesn't notify Standard User of new updates

I am running Home Premium as a Standard User, and have set Windows Update to
"check for updates but let me choose whether to download and install them"

I have found that Windows Update does automatically check for updates, but
it doesn't notify me of new updates as it does when I am logged in as an
Administrator.

I would like to know if this behavior is by design, and if not, what do I
need to do to get it to work correctly.