Minitab – Probability Distributions
Rolling Dice
This lab will involve examining probability distributions and expected values for when one fair die and two fair dice are rolled.
Roll One Fair Die
Let y = the number we see when one fair die is rolled.
Setting Up the Minitab Worksheet
Set up your Minitab worksheet to look similar to the table below.
C1 
C2 
y 
P(y) 
1 
0.166667 
2 
0.166667 
3 
0.166667 
4 
0.166667 
5 
0.166667 
6 
0.166667 
Simulating 1000 Rolls of One Die
Tally Results
Calculate the Mean, Standard Deviation, and Variance
Rolling One Die 1000 More Times
We want to again roll a fair die 1000 times and find the mean, standard deviation, and variance for our new sample. Let z = the number we see when we roll a fair die.
Simulating 1000 Rolls of One Die
Tally Results
Calculate the Mean, Standard Deviation, and Variance
Roll Two Fair Dice
Let x = the sum of the numbers we see when two fair dice are rolled. Therefore, x can be any number from 2 to 12. Fill out the rest of the table below by adding together the results of each row and column.

1 
2 
3 
4 
5 
6 
1 
2 





2 






3 






4 






5 






6 





12 
Setting Up the Minitab Worksheet
Set up the next four columns of your worksheet to look like those below.
C5 
C6 
C7 
C8 
x 
Freq(x) 
P(x) 
xP(x) 




Entering Values for C5
The x column should contain all the possible outcomes for a roll of two fair dice. Therefore, C5 should contain the numbers 2 through 12.
Entering Values for C6
Count the number of time each value of x appears in the table of sums you made for the rolls of two dice.
Calculating C7
Find the Expected Value for x
Simulating 1000 Rolls of Two Dice
Tally Results
Calculate the Mean, Standard Deviation, and Variance
Relationship Between the Means
What do you notice about the means for your sample rolls of one die and two dice? Explain your results. Type your answer into the session window.
Relationship Between the Variances
How is the variance for the roll of one die related to the variance for the roll of two dice? Why would it be difficult to see a relationship between the standard deviations? Explain your results. Type your answer into the session window.
Show in Theory
On a separate piece of paper, show in theory (an argument that would prove any example) the relationship between the means and variances for rolls of one die and two dice.
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