here let X is sum of two scores ;
below is probability distribution of X:
|
x |
f(x) |
xP(x) |
x2P(x) |
|
2.0000 |
  1/36 |
0.056 |
0.111 |
|
3.0000 |
  1/18 |
0.167 |
0.500 |
|
4.0000 |
  1/12 |
0.333 |
1.333 |
|
5.0000 |
  1/9 |
0.556 |
2.778 |
|
6.0000 |
  5/36 |
0.833 |
5.000 |
|
7.0000 |
  1/6 |
1.167 |
8.167 |
|
8.0000 |
  5/36 |
1.111 |
8.889 |
|
9.0000 |
  1/9 |
1.000 |
9.000 |
|
10.0000 |
  1/12 |
0.833 |
8.333 |
|
11.0000 |
  1/18 |
0.611 |
6.722 |
|
12.0000 |
  1/36 |
0.333 |
4.000 |
|
|
total |
7.000 |
54.833 |
|
|
|
|
|
|
|
E(x) =μ= |
ΣxP(x) = |
7.0000 |
|
|
E(x2) = |
Σx2P(x) = |
54.8333 |
|
|
Var(x)=σ2 = |
E(x2)-(E(x))2= |
5.8333 |
|
|
std deviation=Â Â |
     σ= √σ2 = |
2.4152 |
as intelligence score :Y =X+1
hence therefore mean of Y =E(X+1)=E(X)+1 =7+1
=8
and std deviation =SD(X+1)=SD(X)=2.4152
