I've been asked a question of 2 parts, the first part is easy asking when the Poisson distribution acts like a Binomial distribution.
The second part is what is messing me up. It asks: what's the uncertainty in a counting experiment with n counts. Plot the fractional uncertainty vs n counts so that I get a linear graph. I'm given the uncertainties of (10%, 5%, 1%).
My issue is that I know that fractional uncertainty (says in my notes) $1/\sqrt{n}$ so when I plug in my values for my fractional uncertainty (.1, .05, .01) I get the values of n for 100, 400, 10,000. When this is plotted it is not even close to being linear.
Where am I going wrong with my thinking?