Hi,

I have the following problem that comes with the solution, but I don't understand where comes from. Thanks a lot for your help!

The problem and the solution are here:

Problem:

I roll a fair die until I get a six. I do this 120 times. Estimate the probability that I need more than an average of 6.5 rolls each time.

Solution:

Let be the total number of turns needed. Then is the sum of independent RVs with distribution . The CLT gives , so .