I'm performing a radioactivity experiment where I measure a specific number of counts in some time period t.
Later on I take the total count rate. (Number of counts/time: $N/t$)
I'm supposed to find the error in total count rate. My initial impression was to do some sort of standard error measurement and go from there. I've been told, however, that the error in total counts measured is simply the square root of $N$
Why is this the case? I've got the impression it's to do with the data following some sort of distribution or something, but is there an obvious answer that I'm missing?