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That's quite a broad question. The APY will depend on how much money you have in your acount and what kind of account you have. You'll need to visit a few Norwegian banks to find out what they have on offer and compare their products. I think it's usually less than 0.5 percent for a savings account.
The problem is that to open an account in Norway you'll need a Norwegian ID number, which you might not have yet, although your bank can help you get a temporary one for the purposes of opening an account. You can open an account with DnB or with Fokus, but will need to go into an international branch to do so. If there isn't one near you, you should probably just wait until you get to Norway.
DnB and Fokus are the only two banks I know of with web sites in English. See https://www.dnb.no/en/corporate/global-network.html or http://www.fokus.no/nb-no/om-fokus-bank/InEnglish/Pages/in-english.aspx for more on opening an account.
Also have a look at Banking and Taxes in Norway for more information.