Role-playing games like Dungeons & Dragons use many different types of dice. Sup
ID: 3208112 • 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? How spread out are their intelligences, as measured by the standard deviation of the distribution? (Round your answer to four decimal places.)
Explanation / Answer
Result:
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? How spread out are their intelligences, as measured by the standard deviation of the distribution? (Round your answer to four decimal places.)
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
Calculation for mean and sd.
x
p(x)
x*p(x)
(x-mean)^2*p(x)
3
0.015625
0.046875
0.140625
4
0.03125
0.125
0.5
5
0.046875
0.234375
1.171875
6
0.0625
0.375
2.25
7
0.078125
0.546875
3.828125
8
0.09375
0.75
6
9
0.109375
0.984375
8.859375
10
0.125
1.25
12.5
11
0.109375
1.203125
13.23438
12
0.09375
1.125
13.5
13
0.078125
1.015625
13.20313
14
0.0625
0.875
12.25
15
0.046875
0.703125
10.54688
16
0.03125
0.5
8
17
0.015625
0.265625
4.515625
Total
1.000
10
110.5000
Average =10
Variance=110.5000
Standard deviation : 10.5119
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
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.