A graph showing normal distribution over Time variable

Hi and welcome. Do you have the distribution already ?

If you're asking how to set it up I'd put my time data in column A using 120 rows being one row for each 1 min increment between 4pm and 6pm. I'd put my distribution data in column B and chart this data.

Have I understood your dilemma? If not provide some more info.

normal distribution curve.xlsx

I'm still not 100% clear on what you want but look at this. It represents 1000 students distributed over a 3 hour period. I have also created a cumulative column so you can see at what time a particular threshold might be reached.

OK. Lets start with the explanation first.

You have 180 rows of data for a three hour spread with 1 minute intervals.

A normal distribution curve is normally drawn showing + and - 3 standard deviations but in reality it is asymptopic so it never ends. I decided to go to 4 stadard deviations just to be sure.

So in column A I created your time intervals starting at 4 pm (16:00:00) and incrementing by 1 minute. The easieist way to do this is to type 16:00:00 into the first cell and Excel will recognise this as a time format. It actuall stores it as 0.666667 because this is what 16 divided by 24 is decimally. Now in the cell below that I typed 16:01:00 and again excel recognises this as a time. Highlighting both cells you can drag down to fill the full 180 rows with all the times you require.

In column B I wanted to put equivalent x axis normal distribution figures in. As I said above I wanted it to span from -4 to 4. This is a range of 8 across 180 cells so the interval between cells was 0.0444444. Again starting with the first cell in column B I typed in -4 then the next cell, -4 +0.0444 = -3.955556. Draging and copying these down the full 180 rows gave me my normal distribution range of x values.

The Normdist formula in column C takes the value in column B, applies a mean of 0 (ie centres the curve on 0) and a standard deviation of 1 (so that 1 in my x axis is equal to 1 SD) and gives me a corresponding y value. Now the area under a normal distribution chart will = 1. If you add all the values up you actually get 22.5. Why? because the area is actually the sum of all the numbers multiplied by the width of each increment. In this instance each increment isn't 1 but is 0.04444. So we have to correct for the width of the increments not being 1. If we multiply by 0.044444 its actually the same as dividing by 22.5 (i was just a bit sloppy with my arithmetic before and was working backwards and I think I only used 0.044 rounded too early and got a slight error). Applying this correction factor to each cells in column C ensures the area under the curve (or all the sum of the individual values is equal to 1). Then becasue you wanted to use 1000 students I simply multiplied each cell by 1000 to factor it up.

Interestingly this took me longer to write the explanation than it did to create the sheet

Now to work out how to make it variable for you. I may not get a chance today but I'll see what I can do

normal distribution curve.xlsx

Didn't take as long as I thought.

Enter variables into the yellow shaded cells - student number, start time and stop time.

To answer your question above, the chart is a scatter chart. When you enter a range of data that is a time series it automatically uses time formats in the x axis.

normal distribution curve.xlsx

The web site was playing up. This should do what you want. Use the sd number to make your graph shorter and wider numbers greater than 1 or slimmer and taller - numbers less than 1. I left teh baseline graphs in so you can see.
If you use Sd numbers of say 0.8 to 1.2 the cumulative will stay about right but if you start putting in big numbers - say 3 or 4 then you'll notice hte cumulative doesn't add up to the total. this is because you're pushing the tails of the graph out beyond the calcualted range

Great. Glad it worked for you