Probability of a multiple variables sum

Hi everyone,

I’m coming here for really advance statistic/probability advice.
I would like to know the probability of a variable TAU_total such as TAU_total=TAU1+TAU2+….+TAU129.
The variables TAUi are independent of each other.
For each one of them, I have a sample of 20,000 values which you can see some examples of their distribution on the histograms in the attachment.
My question is the following: I would like to be able to determine the probability of TAU_total to be superior to a certain value Xmax.

Thank you for your help,