Answer
See graph and data below.
$\mu=7$
$\sigma^2=5.83$
$\sigma=2.41$
Work Step by Step
Roll two dice and add up the face numbers.
(a). Total possible outcomes = $6\times6=36$
(b). Sums (S) and possible favorable outcomes for each sum are listed below:
S Fav. Outcome
2 11
3 12-21
4 13-22-31
5 14-23-32-41
6 15-24-33-42-51
7 16-25-34-43-52-61
8 26-35-44-53-62
9 36-45-54-63
10 46-55-64
11 56-65
12 66
(c). The sum (S) and their probabilities (#fav.outcome/36) are listed below:
S Probability
2 0.027777778
3 0.055555556
4 0.083333333
5 0.111111111
6 0.138888889
7 0.166666667
8 0.138888889
9 0.111111111
10 0.083333333
11 0.055555556
12 0.027777778
(d) the above probabilities form the distribution as shown in the figure
for the sum shown on the faces when two dice are rolled.
(e) The mean, variance and standard deviation can be calculated using formulas as the following:
$\mu=7$
$\sigma^2=5.83$
$\sigma=2.41$
