My new apartment has no 3 prong plugs with ground

Landlords love tenants who complain to the local government about trivial stuff. Best way to get a rent increase i know of.
And if you complain enough, you get evicted. NOT by the landlord, by the same government agency. "This place is 'unfit for human habitation', no one can live here, you have ten days to move out". REALLY. (been there, and had it happen, even though MY apt was fine, they just boarded up the whole building... ) So be certain to really complain loud and often about every trivial thing...

Or, at minumum...
"Gee, we had to get this work done.. so now your rent has to go up 30%. Sorry".

And in my shared 15 amp single circuit apartment I never had any problems for my large stereo. Only my small microwave and the guy next doors' hair dryer seems to not get along.

@Mr J- I should have prefaced/qualified that statement with, "In most older homes:" OOPS!

Pre-war 2-prong wireing imposes a danger of setting building on fire and needs to be rewired new. Any tenant ringing a bell should not be neglected weather landlord loves or hates such. No matter how many amps you've got you may only use it OK for small appliances and microwaves, iron, corded drills may easily set these old wires on fire.

Fellas, we don't know for sure if the wiring in the duplex dwelling is nob and tube or not.

The wire could be old two wire cloth and paper covered thermoplastic insulation covered wire. Which should be noted could be very brittle and crack and break off if disturbed inside the recept electrical box. ( Degree is how much heat the wires were subjected to over the years from connected loads to the receptacle. Heat also caused from poor contact pressure between the recept and the inserted plug and the amount of connected load.)

The wiring could even be the early version NM, Romex is a trade name, with a plastic outer covering with thermoplastic insulation covering the two copper conductors

What ever it is it could still be safe in the eyes of the AHJ, authority having jurisdiction, in the area.

In many AHJ jurisdictions old wiring does not have to be brought up to meet current code unless a new electrical service is being upgraded or a major remodel where new wiring would be installed. Even then it depends on the AHJ.

In my metro area landlords of rental properties must have the property inspected by the AHJ and issued an occupancy permit before renting the dwelling unit to the public.
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EJS, you can easily determine whether or not the screw that holds the wall plate over the outlet is grounded, by using a multimeter or a cheap neon bulb AC tester to see if 120 volts or so exists between that screw and one of the two slots in the receptacle (the smaller one if they are unequal in size).

Obviously, if you do that don't touch the metal tips at the end of the test leads while they are in contact with the outlet.

According to this Wikipedia article, knob and tube wiring was in common use in North America "from about 1880 to the 1930s."

Regards,
-- Al