Question

1. Roll two dice 48 times and record the sum of the spots on the top faces as you roll. Then construct a probability distribution for your 48 sums. Using the probability distribution, you constructed, find the mean number of spots. (If you don't have two dice, then cut out 6 pieces of paper with each being the same size and with #1,2,3,4,5,6 written on them. Place the pieces of paper in a hat or bowl. Pull out a number, then replace, pull out a number again and record the sum of the 2 numbers.)

Answer 1

Roll #	Die 1	Die 2	Sum
1	3	1	4
2	3	3	6
3	3	1	4
4	6	6	12
5	6	3	9
6	6	6	12
7	4	6	10
8	6	6	12
9	4	6	10
10	5	2	7
11	4	2	6
12	5	2	7
13	1	1	2
14	1	5	6
15	5	1	6
16	3	3	6
17	5	6	11
18	4	1	5
19	6	1	7
20	1	3	4
21	5	1	6
22	2	1	3
23	2	6	8
24	2	5	7
25	1	2	3
26	1	1	2
27	3	3	6
28	1	3	4
29	3	5	8
30	3	4	7
31	5	1	6
32	5	2	7
33	5	5	10
34	3	4	7
35	5	3	8
36	3	3	6
37	6	2	8
38	6	5	11
39	4	4	8
40	4	1	5
41	5	6	11
42	2	5	7
43	2	2	4
44	1	1	2
45	4	4	8
46	6	5	11
47	5	3	8
48	5	6	11

Sum (x)	Frequency	Probability P(x)	x P(x)
2	3	0.063	0.125
3	2	0.042	0.125
4	5	0.104	0.417
5	2	0.042	0.208
6	9	0.188	1.125
7	8	0.167	1.167
8	7	0.146	1.167
9	1	0.021	0.188
10	3	0.063	0.625
11	5	0.104	1.146
12	3	0.063	0.750
		∑ x P(x) =	7.042

Mean number of spots = 7.042

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