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My question relates to gamma spectroscopy. I understand how the net peak area is calculated for any photopeak. Fortunately, gamma-spec software (e.g., Genie-2000 from Canberra) provides Net peak area and associated uncertainty (for Cs-137 661.7 keV peak, as an example). My question: are the values between extremes uniformly distributed? For example, for a hypothetical case with net peak area 1000+/-99, the net peak area can vary between 901 and 1099. So, the values between these extremes are uniformly distributed? In other words, if the experiment is repeated, the probability of getting any peak area between (901,1099) is same? Or is it biased at the centroid (1000)—such that centroid peak area will occur most of the times and the extremes will occur least (like Gaussian nature)?

I am confused because the 'Gaussian Shape' of the photopeak is already accounted to calculate the net peak area?

Thanks,