https://mathworld.wolfram.com/Dice.html
How does one find the error of a sum of four or five 6-sided dice probability distribution in relation to the Normal Distribution?
2026-03-28 19:37:53.1774726673
Dice Sum Probabilities and The Normal Distribution
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Personally, I would start by just plotting the exact pdf and the normal approximation, shown for 5 dice, below:
Then if you want to examine the errors more closely (defined as the exact value minus the approximation), I would plot those too.
Notice the vertical scale--the errors are fairly small.