Have you followed up with the manager and informed her that the letter did nothing to lower the noise level? She's not going to know unless you tell her.

Document, document, document. Keep a list of what type of noise, when it happens and how it affects you.

11:30 pm. Bouncing balls overhead. Woke me up.
7 am. Jumping and running. Couldn't hear news on TV set to normal volume.

That sort of thing. Some of what you are hearing is, unfortunately, just what you have to accept with apartment life in the US--footsteps, doors closing, etc. But there is noise and there is excessively loud noise. And the really loud noise can be controlled.

See if you can get the manager to come over to your place while the noise is happening. That might help.

But I'd start investigating other apartments that have better noise control and make plans to move when your lease is up. There's a newborn baby living below me and I only hear her cry when the windows are open. It *is* possible to have an apartment when every single little sound doesn't carry.

I had the same problem as you & ended up having to move. The office manager refused to do anything about my horrible upstairs neighbors. I also tried calling the police but it never did any good. In the meantime, my health was suffering due to lack of sleep & the stress of living with constant noise. I got fed up with it & moved to a quiet place. I have no neighbors & am on the top floor. You may have to move to get some peace & quiet! Best of luck to you!