# Solved – Interpreting Results of Poisson Distribution

I'm using the Poisson distribution to predict the number of concurrent users accessing a website. The method is described in a paper by Eric Man Wong.

This paper provides a formula for calculating the average number of concurrent users as the number of users multiplied by their time on the website divided by length of day. For example, 100 users access a system for 30 minutes during a day of length 480 minutes will have an average of 6.250 concurrent users (100 * 30 / 480).

From this I use the POISSON.DIST function in Excel to calculate the probabilities of a range of concurrent users. So for 13 concurrent users I use POISSON.DIST(13, 6.250, false) which gives 0.688%.

My question is how do I interpret this result. Does it mean that within any one day we should expect to see 13 concurrent users for 0.688% of the time (480*0.00688 = 3.3 minutes) Or in any one day there is 0.688% chance of 13 concurrent users which means that we can expect to see 13 concurrent users once every 145 days (1/0.00688).

The table generated in Excel is below

`Concurrent  Probability Users   0           0.19305%   1           1.20653%  2           3.77042%  3           7.85504%  4          12.27350%  5          15.34187%  6          15.98112%  7          14.26885%  8          11.14754%  9           7.74135% 10           4.83834% 11           2.74906% 12           1.43180% 13           0.68837% 14           0.30731% 15           0.12804% 16           0.05002% 17           0.01839% 18           0.00638% 19           0.00210% 20           0.00066% `
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It would probably be good to make a table of number of users and %. In `R` this can be done with
``n <- 0:30 probs <- dpois(0:30, 6.25) tablepois <- cbind(n, round(probs*100,2)) tablepois ``