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Question

# What is the expected result when you roll a single die? Specify 40 rolls, and then click on "roll the dice." After the last roll, click on "show mean." Does your expected sum agree with the green mean? What happens to the plotted points as the number of rolls increases? If the picture is not clear, click on "roll the dice" for a new total of 80 rolls. Describe what you see in a sentence. What is the name for this principle?

Solution

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Your expected sum (mean) will most likely not agree with the green mean of 3.5, but will be relatively close in value.

As the number of points increase, the distribution will become more and more uniform (height of the bars will be roughly the same).

This is the principle of the law of large number, that is as the number of simulations increases, the sampling distribution will approximate the theoretical distribution.

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