How do the results of your simulated roll and experimental roll compare?
Do you think the computer-based roll provides an accurate simulation of actual rolls?
Make a bar graph of the sorted rolls from both the 100 sorted randomly generated rolls and the 10 experimental rolls. Refer to
Technical Hints on how to make a distribution bar graph.
Which sum occurred most frequently when you rolled 10 times? Which occurred most frequently when you rolled 100 times? If they are different, how can you explain the difference.
How do each of the graphs you made compare to your histogram of possible rolls? Do they reflect the results you expected?
How do the graphs for 10 rolls and 100 rolls compare? What conclusions can you make about how well the Law of Large Numbers applies to rolling number cubes? If necessary, refer back to "Introduction" for an explanation of the the Law of Large Numbers.
Did your data for 100 rolls match the theoretical probability exactly? If not, what do you think would happen if we combined the results of the class so that there were1000 rolls? Open a new spreadsheet. Refer to Technical Hints on how to use a spreadsheet. In Column 1 list the possible sums for rolling two cubes, 2-12. Now, using data collected from each class group list the number of times each sum occurred in Column 2. Following the same procedure you used earlier use the data in Column 2 to make a bar graph for 1000 rolls.
In Column 3 calculate the probability of each sum occurring.
Compare the experimental data for 100, 1000 rolls, and the theoretical probability. Write a paragraph that describes your analysis and conclusions.
