When can I expect to hear back?

i am going for cadet and finished jst, and my written as well as everything else. Only thing I have left to do is oral psych. I know its backed up but I just sent a email a couple days ago topsychoralscheduling@nypd.org and im wondering when I can expect a follow up email scheduling me and if this is in fact the right email I was supposed to contact. Is it normal for them to not schedule you right after you finish the written? Im not sure why I wasnt selected and havent received any follow up emails yet

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