Lets use Excel to simulate rolling two 8-sided dice and findingthe rolled sum.
• Open a new Excel document.
• Click on cell A1, then click on the function icon fx andselect Math&Trig, then select RANDBETWEEN.
• In the dialog box, enter 1 for bottom and enter 8 for top.
• After getting the random number in the first cell, click andhold down the mouse button to drag the lower right corner of thisfirst cell, and pull it down the column until 25 cells arehighlighted. When you release the mouse button, all 25 randomnumbers should be present.
• Repeat these four steps for the second column, starting incell B1.
• Put the rolled sum of two dice in the third column: Highlightthe first two cells in the first row and click on AutoSum icon.Once you receive the sum of two values in the third cell, drag thelower right corner of this cell, C1, down to C25. This will copythe formula for all 25 rows. We now have 25 trials of ourexperiment.
Once these steps are completed, attach a screenshot of yourExcel file to your assignment.
(a) Find the theoretical probability that the rolled sum of bothdice is 8.
(b) Based on the results of our experiment of 25 trials, obtainthe relative frequency approximation to the probability found in(a). You can do so in Excel in two different ways: i) create thehistogram of the third column data, then scroll the mouse over therelevant bar - this will give you the frequency with which you candetermine the relative frequency; or ii) in a cell, type thefunction COUNTIF(C1:C25,8)
(c) Generate the frequency distribution histogram of yourexperiment of 25 trials, and copy it to a Word document. Make sureto add a title to your histogram.
(d) Repeat the simulation for 100 and 1000 trials, and calculatethe relative frequency for each, and create the frequencydistribution histogram - resize the 3 histograms so that all 3 fitbeside each other in a row.
(e) Identify which of the 3 relative frequencies for ’8’ is theclosest value to the theoretical probability found in (a). Brieflyexplain how these experiments demonstrate the Law of LargeNumbers.
(f) Identify the shape of the probability distribution (uniform,bell-curved, right-skewed or left-skewed).
