Question Part Points Submissions Used Role-playing games like Dungeons & Dragons

Question

Question Part Points Submissions Used 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 How spread out are their intelligences, as measured by the standard deviation of the distribution? (Round your answer to four decimal places.)

Explanation / Answer

Let D1 be die roll 1 and D2 be die roll 2.

The mean of rolling a single 8 sided die is, 1 = (1+2+3+4+5+6+7+8)*(1/8) = 4.5
The 12 = [(1-4.5)2 + (2-4.5)2 + (3-4.5)2 + (4-4.5)2 + (5-4.5)2 + (6-4.5)2 + (7-4.5)2 + (8-4.5)2](1/8) = 5.25
Then for the sum Intelligence, I = D1 + D2 + 1, I = 2*1 + 1 = 10
I2 = 2*1 = 2*5.25 = 10.5, I = sqrt(10.5) = 3.2404

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