The sum of two dice - probability simulation using Excel

Theoretical out come of the sum of two dice is first carried out. This is then plotted to observe the binomial distribution characteristics - reflecting in the limit, the normal distribution shape. This is achieved by using all 36 probable outcomes. However, when a simulation is carried out (experiment), the binomial distribution shape is achieved only if the sample size is increased. This experiment reinforces the importance of sample size when probability investigation is carried.

All the probable outcome of the throw of two dice is:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2.1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Experimentally (simulation), 36 throws will unlikely to achieve the the theoretical outcome probabilities, unless the sample size is increased a great deal. Again what the optimum sample size would be, will be a question of compromise, as the sample size is increased, the more probable it becomes to achieving the shape of the theoretical distribution. But, one has to keep in mind the cost attached to unnecessarily large data size.