can someone please tell me how to solve this statistics problem?

Question

i have been stuck on it for two days!

A die is continuously rolled until the total sum of all rolls exceeds 225. What is the probability that at least 70 rolls are necessary?

can someone please help me! thanks

Answer 1

E(of one roll)=3.5
Var one roll= 1/6*(Sigma(j=from 1 to 6) (j-3.5)^2)=2.916666
since you roll the dice 70 times you may use Normal approximation for the distribution
E(70 rolls)=70*3.5=245
var (70 rolls)=2.916666*70
sd(70 rolls)=(2.916666*70)^.5=14.28

What is the probability that you did not reach 225
225 is 20 points under the expected 245 and
is 20/14.28 =1.4sd standard deviations less then the expected
assuming normal distribution
p(225)=p((225-245)/14.28) under standardized normal distribution x~N(0,1) look it up in the normal distribution table. this is the probability that 70 is not enough. You need to look up the area from - infinity to -1.4
1-the probability that it is not enough is the probability that it is enough.

Answer 2

If P(n) is the probability that the sum will exceed 225 in n rolls,
225
∑ P(n) = 160.952381
n = 38
225
∑ P(n) = 156.6518252
n = 70
156.6518252/160.952381 = 0.973280571

Answer 3

1/2 if you rolled the same number every time.