That works for a conservative estimate of continuous load.
So long as your appliances are similar - for instance, microwaves come in a range of wattages.
Check appliance labels for a better max load figure.
You may be able to get by with lower wattage inverter, for instance by not running microwave and coffee pot at the same time.
Most of us have quite a few high power appliances, but don't use many at once.
Do you have any appliances with large motors? That could include water pump, circular saw, etc.
Motors typically draw 5x their nameplate rating, for a fraction of a second. If the inverter can't supply this, it shuts off.
Some inverters give a surge rating. If the rating is for 30 milliseconds, that isn't long enough to help. If it is for 3 seconds, then it is good.
All this goes to size the inverter. And current draw the batteries must supply. It is in units of Watts, or of kW.
Beyond that, you need to know how many minutes or hours each will run in a day. Determine watt-hours or kWh.
That is used to size PV array and battery storage capacity.
That's a good number to work with, for inverter. But still a pretty good size inverter. How many minutes do you need to draw all 3800A? Some inverters can provide higher wattage for a few minutes before getting too hot, so maybe a 2500W or 3000W inverter could do it. Or, a 4000W to 5000W inverter could be used for continuous operation.
Any 240V loads, or all 120V?
Here's one of the lower cost brands:
store.santansolar.com