Question

(1 point) A die s continuously rolled until the total sum of all rolls exceeds 175 What is the probability that at least 55 rolls are necessary? 0.1423

Please show work so i can understand it. Thank you!

Answer 1

for a single roll each outcomes has equal probbaility =1/6

x	f(x)	xP(x)	x2P(x)
1	1/6	0.167	0.167
2	1/6	0.333	0.667
3	1/6	0.500	1.500
4	1/6	0.667	2.667
5	1/6	0.833	4.167
6	1/6	1.000	6.000
	total	3.500	15.167
	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

hence for 54 rolls ; expected total =54*3.5=189

and std deviation =1.7078*sqrt(54)=12.55

therefore P(that for 55 rolls sum is at most 175)= P(X<175)=P(Z<(175.5-189)/12.55)=P(Z<-1.08)=0.1401

( please revert for any clarifcation)