Tossing Coins is a Better Idea
So a better model is tossing coins a 1000 times.
Shift over coin toss by 200 so results lie in range 201..1200 as in the Dice accumulation.
Now the frequency distribution is narrower.
It is still a beautiful bell shaped Gaussian but the percentage error is 1.6% not 2.4%.
You will get better answers from asking 1 person from 1000 households rather than 5 people from each of 200 households.
Actually Dice are not a very good representation of polling, as a result with 1000 cells corresponds to only 200 Dice
This is like polling where you went to 200 households and asked 5 people in each household. It is not 1000 independent samples.
1000 Tosses Count Number of Heads