Create bell curve with a discrete variable

#1
Hello everyone,

I like stats but I must warn you that I am far from an expert so please forgive me if my question is a bit basic :).

My issue is the following: I ran a simple randomized experiment on a population of 151,173 users. The users were exposed to a display banner on the internet and we recorded the numbers of clicks on this banner. The result was 2,791 clicks.
So the click rate is 1.85%

Now what I want to do is to create confidence intervals and a bell curve showing the distribution of the possible result (if possible centered on 1.85%).
I tried to use the Agresti-Coull method and got the following results:
- Upper 95% Confidence Limit = 1.92%
- Lower 95% Confidence Limit = 1.78%

I am happy with this interval but i am at loss when it comes to create the bell curve.
I tried to calculate a standard variation using x=1 when there is a click and x=0 when there is no click but I couldn't get further than that.

Any helps or tips much appreciated.

Kind regards,

Clement
 

maartenbuis

TS Contributor
#2
A bell curve is for a continuous variable, in your case you can have ..., 2,790, 2,791, 2,793, ... clicks but not 2,791.5 clicks. This translates to a specific set of rates that are possible.