Multiply the voltage by the amperage (current) draw... so 120Vx2.5 = 300...so the fridge draws about 300 Watts when running. How many hours a day will it run? Lets say, maybe in a bad case, 25% of the time...so 6 hours a day. 300W/12V=25 amps, times 6 is 150Ah. I think this is more than it would actually run, but you ought to test it. Get a Kill A Watt meter and plug in your fridge, to measure it for a few days. That will give you the most accurate usage.
Now, will your system run that? As to start up, sure. Your 3000W inverter is more than enough and the starting current draw is brief, so I left it out of the calculations...we're close enough. As to day-to-day demands, we'd need more information. To start with, what kind of batteries do you have? 360Ah in FLA (regular lead acid) batteries gives you about 180Ah of usable energy. Lithiums will yield more.
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