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The cost of living in Norway is steep, as much as double what it is in the States. But it always depends on your own standards and lifestyle, so it's a hard question to answer somtimes.
I suggest you make a note of what you consider essentials and compare it to the table on the Expat Arrivals Cost of Living in Norway page. This will give you a good idea of the minimum amount you'll need to be comfortable.
Also check out the pages on Accommodation in Oslo for more on the cost of a small bachelor flat in Oslo. A one-room flat in the city centre will cost upwards of 6,000 NOK.