# Error in total counts

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?

• This comes from the central limit theorem. There is a nice if somewhat detailed discussion of this on the Stats SE. – John Rennie Oct 8 '15 at 10:34
• Thanks @John Rennie. I do now also have a simpler answer to my question but I'm not sure about posting it as I've been making a habit of answering my own questions lately! Better to delete the question or answer it myself? – Matt Oct 8 '15 at 11:49
• Answer it yourself. If it's a good answer then it will help future visitors to the site and earn you some rep :-) – John Rennie Oct 8 '15 at 11:56