Question

role playing games like dungeons & dragons use many different types of dice. suppose that a SIX sided die has faces marked 1,2,3,4,5,6. 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 intelligence , as measured by the standard deviation of the distribution?(round your answer to four decimal places)

Answer 1

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=	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