Question

(1 point) A dice is continuously rolled 64 times. What is the probability that the total sum of all rolls does not exceed 200?

Hint: Start by computing the mean and the standard deviation for 1 dice roll.

Answer 1

for a single dice:

x	f(x)	xP(x)	x2P(x)
1	1/6	0.1667	0.1667
2	1/6	0.3333	0.6667
3	1/6	0.5000	1.5000
4	1/6	0.6667	2.6667
5	1/6	0.8333	4.1667
6	1/6	1.0000	6.0000
	total	3.5000	15.1667
	E(x) =μ=	ΣxP(x) =	3.5000
	E(x2) =	Σx2P(x) =	15.1667
	Var(x)=σ2 =	E(x2)-(E(x))2=	2.9167
	std deviation=	σ= √σ2 =	1.7078

expected sum of 64 rolls=64*3.5= 224

and stndard deviation =1.7078*√64 =13.6624

probability that the total sum of all rolls does not exceed 200 =P(X<200)=P(Z<(200-224)/13.6624)

=P(Z<-1.76)=0.0392