!@#%#$ Math

[bcholmes]

Okay, I can't figure out the math on this problem. Can anyone help me?

I have a bunch'a numbers. Response times from a web server. I round off these response times into nice numbers. Closest 100 milliseconds or sumpthin. For every 100 millisecond interval, I count the number of occurences, giving me a pretty graph, like this.

Now I want to do standard deviation stuff. I calculate the standard deviation of the response times. Turns out, in my case, to be about 300 milliseconds. Big spread. Clustered in the [0s-0.5s] range.

Now, standard deviations are ideal for drawing the dreaded bell curves:

And I know that for each sigma, we're covering a larger percentage of the occurrences. In the following picture, for example:

the red area is supposed to cover something like 68% of the data, if the arrow marks out one sigma.

What I ultimately want to do is to render a graph with the standard deviation curve superimposed over the bar chart:

My question: how the hell do I calculate meaningful Y values for the standard deviation curve? I figure that the mid-point should be 50% of my total number of occurrences. How do I get the other points?

(Did I mention that I didn't do all that well in statistics? Or Fourier Analysis, but that's a whole 'nuther story).