Article: The central limit theorem states that the sum of a number of identical dice approaches a normal distribution as the number of dice increases. Assuming n dice numbered 1 to r, the formulas below apply.  The mean is  (r+1)/2. The variance is n(r^2-1)/12. The standard deviation is the square root of the variance.
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For a large number of dice, exact computation by the above methods may be difficult. Compute the mean and standard variation based on the number and type of dice. Use the normal distribution with the above mean and standard deviation as an approximation of the sum of the dice.