Given your itinerary, you will need to enter the Schengen area in Amsterdam no matter what (even if you had a very short layover and no intent to visit the city). Once you have done that, there is nothing physically stopping you from going to the city (there are one-way doors between the Schengen part of the airport and the luggage claim area and exits but no passport check).
Your visa almost certainly allows that (a regular Schengen visa does, as do various long-stay visas from Schengen member states). It's very common, I would not expect any problem, especially if you can show your tickets, etc. to explain why you have a Norwegian visa.
Even if you had an unusual visa (e.g. a so-called “limited territorial validity” visa), a transit visa would not help you.