Role-playing games like Dungeons & Dragons use many different types of dice. Sup
ID: 3208372 • Letter: R
Question
Role-playing games like Dungeons & Dragons use many different types of dice. Suppose that a eight-sided die has faces marked
1, 2, 3, 4, 5, 6, 7, 8.
The intelligence of a character is determined by rolling this die twice and adding 1 to the sum of the spots. The faces are equally likely and the two rolls are independent. What is the average (mean) intelligence for such characters?
10 was correct!
How spread out are their intelligences, as measured by the standard deviation of the distribution? (Round your answer to four decimal places.)
3.2400 was incorrect
Explanation / Answer
Sample space: adding 1 to the sum of the spots
FACES
one
two
three
four
five
six
seven
eight
one
3
4
5
6
7
8
9
10
two
4
5
6
7
8
9
10
11
three
5
6
7
8
9
10
11
12
four
6
7
8
9
10
11
12
13
five
7
8
9
10
11
12
13
14
six
8
9
10
11
12
13
14
15
seven
9
10
11
12
13
14
15
16
eight
10
11
12
13
14
15
16
17
Probability distribution
Number
f
p
3
1
0.0156
4
2
0.0313
5
3
0.0469
6
4
0.0625
7
5
0.0781
8
6
0.0938
9
7
0.1094
10
8
0.1250
11
7
0.1094
12
6
0.0938
13
5
0.0781
14
4
0.0625
15
3
0.0469
16
2
0.0313
17
1
0.0156
64
x
p(x)
x*p(x)
(x-mean)^2*p(x)
3
0.015625
0.046875
0.765625
4
0.03125
0.125
1.125
5
0.046875
0.234375
1.171875
6
0.0625
0.375
1
7
0.078125
0.546875
0.703125
8
0.09375
0.75
0.375
9
0.109375
0.984375
0.109375
10
0.125
1.25
0
11
0.109375
1.203125
0.109375
12
0.09375
1.125
0.375
13
0.078125
1.015625
0.703125
14
0.0625
0.875
1
15
0.046875
0.703125
1.171875
16
0.03125
0.5
1.125
17
0.015625
0.265625
0.765625
Total
10
10.5
Average =10
Variance=10.5000
Standard deviation :3.2404
FACES
one
two
three
four
five
six
seven
eight
one
3
4
5
6
7
8
9
10
two
4
5
6
7
8
9
10
11
three
5
6
7
8
9
10
11
12
four
6
7
8
9
10
11
12
13
five
7
8
9
10
11
12
13
14
six
8
9
10
11
12
13
14
15
seven
9
10
11
12
13
14
15
16
eight
10
11
12
13
14
15
16
17
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