any 3 prong 110v outlet should be physically grounded to a grounded
box.
chances are there is no ground available at the metal box.
there are testers for this if you have no meter.
if you have a meter measure 110v hot prong is smaller to the metal box.
larger prong is common terminal.

see:

blackcat wrote:
I have two-prong outlet(old outlet) and like to change to grounding
three-prong outlet. Since I have a lot of
appliance that require three-prong outlet. I know I can use connector
to covert to three-prong. I would
rather change the power outlet.
I got a three-prong grounding outlet from Home Depot. Some people say
that I can just wire the third wire to the metal box and
the grounding outlet, but some people consider I should not do that it
is not safe.

Should I just wire the third wire, connect between metal box and the
three-prong grounding outlet?

Thanks