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I was under the impression that NYC had a confirmed infection rate of ~1%. Have they really had a tenth of confirmed cases die already?

No. Currently >200k confirmed, <11k deaths in New York State.

NY population is 18.8M. 0.05% of the population has died.

New York City's population is around 8.5 M, and more then 10,000 people there have died from from the virus so far (https://www.nytimes.com/2020/04/14/nyregion/new-york-coronav...). That puts the toll over 0.1 %.

I cited the correct, current numbers for the entire state.

You’re citing numbers released by the city where they haven’t confirmed cases, so it doesn’t answer the OP’s question.

Can you cite them, rather than saying that you cited them?