Chapter 11.3, Problem 3A

Solution

To plot: The graph of the theoretical probabilities of getting a sum of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 when two standard dice are rolled.

The graph of the theoretical probabilities of getting a sum of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 when two standard dice are rolled is shown below

  

Given:

The table with frequency and theoretical probabilities of the sum of numbers when two dice are rolled is shown below

Sum	Frequency	Probability
2	1	$\frac{1}{36}=0.0278$
3	2	$\frac{2}{36}=0.0556$
4	3	$\frac{3}{36}=0.0833$
5	4	$\frac{4}{36}=0.1111$
6	5	$\frac{5}{36}=0.1389$
7	6	$\frac{6}{36}=0.1667$
8	5	$\frac{5}{36}=0.1389$
9	4	$\frac{4}{36}=0.1111$
10	3	$\frac{3}{36}=0.0833$
11	2	$\frac{2}{36}=0.0556$
12	1	$\frac{1}{36}=0.0278$

Plot:

The following steps are followed to plot the theoretical probabilities of sum on two dice.

1. Enter the data in an excel sheet in two columns (sum and Theoretical probabilities in decimal form) as shown below

Sum	Probability
2	0.0278
3	0.0556
4	0.0833
5	0.1111
6	0.1389
7	0.1667
8	0.1389
9	0.1111
10	0.0833
11	0.0556
12	0.0278

2. Select the data and insert a scatterplot in excel.
3. Label the horizontal axis as Sum and the vertical axis as Theoretical probabilities.
4. The format of the vertical axis or Theoretical probabilities can be changed to fractions and the graph is shown below