Question:

 We have been trying to calculate the number of PV panels and batteries
 required to use on a stand alone system in a 5 sun hour per day area to
 provide 2000 KWH a month with a 4 day storage for cloudy days.

Answer:

First, How Many Batteries
2000 KWH/mo
Divide by 30 days 66.67 KWH/day
Times 4 days storage 266.67 KWH/daH
Multiply by 1000 for WH 266666.67 Watt Hours
Divide by 12 volts for AH 22222.22 Amp Hours
Divide by 200 Ah Batteries 111.11 200 AH Batteries

Now, going back to 66.67 KWH/day
Divide by 5 hours per day 13.33 KW to be generated for 5 hours
Multiply by 1000 13333.33 watts for 5 hours per day sun
Divide by 12 volts 1111.11 Amperes solar output
Divide by 3 amps 370.37 Harbor Freight 45 watt panel sets

Note, that this does not take any inefficiencies into account so in
practice you would need 10-20% more batteries and solar panels than
this shows. You also didn't say how often those 4 day cloudy periods
occur - in practice you need enough extra capacity to charge those
batteries on top of your daily usage, so the estimate for solar panels
could be low by another 20% or more.

Mostly this shows that the cheapest solar power you can make is the
power you DON'T consume and don't need to make. So, the first step is
always to figure out how little energy you can thrive on and then
design a system to exceed that.

Of course, once you are conserving to that level you may find the
resulting electric bill, and, for that matter, your carbon footprint,
might not justify further action. On the other hand, you may, like
many on this list, be far away from the grid or just want nothing to
do with connecting up.