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So, after a bit of research, I'd say that Peter's nursing education was at the very least a BSN or possibly starting working on an MSN, because in NYC a Paramedic is an EMT-4 level (the highest EMT position) and requires something like 2 years of training! Since he's doing the job after only 2 months and obviously isn't being treated like a 'probie', he's got to have already had a lot of the education.
Of course, it could also be the writers have their heads up their asses again -- these ARE the same people who thought it would be okay to smash a cabinet full of virus samples with NO ill effects.
We really shouldn't expect them to follow Real World logic anywhere. However, I'm going to say that my boy has had some fairly extensive training until/unless the writers say definitively otherwise.