To clarify: We are given 7 serial numbers based on a value n which is unknown (this number is given only to check how good our process of determining n is and to generate the 7 random serial numbers from it).
My process first finds the standard deviation of the given serial numbers. Then I find a limit that n definitely cannot exceed (three standard deviations above the mean) and a max from the given list as what it can't be below. I then simulate what random serial numbers would be generated from the predicted n from the range I found out. I take the standard deviation of each simulation and find which one is the closest to the standard deviation of the given serial numbers and store the corresponding guessed n. I do this x times (the more the better - I used 100) to get x guessed n 's. I take the mean of those guesses to get my final guess. I then find the percent error of my guess based on the actual number.
