A bank wishes to detect high-value credit card frauds. To do this, she analyzes "extreme value" debits made by customers to determine the threshold at which an alert should be triggered and customer confirmation requested. She receives 177 000 000 transactions every month. In a first examination, you would like to choose a threshold using the "Peak Over Threshold" (POT) method for the amount triggering an alert.

We have seen that a common practice is to keep the  largest values of the data to apply the POT method, and that for this choice of , 3 mathematical formulas are commonly used.

We ask you to choose one of these 3 formulas and propose a number representing the quantity of the most significant transactions to retain for our study.

So, there are 3 possible answers, and all 3 are considered correct for the valuation of this question.

You propose and you write an integer number. We will consider any rounding problems you may encounter.

Be careful, if you find something like 23580, you don't write 23,580 nor 25 580, but 23580.