Here’s the Scenario:
Based on our observations over a month, we find that there are 40 dogs on average in a off-leash park during an hour’s time-frame during the day in its open hours.
We want to find out the chance of having a specific number of dogs at any given time in the park during the day (#1).
And we also want to know the chance of having a maximum number of dogs at any given time in the park during the day (#2).
We want to use this data to determine the cost of maintenance of the park, staffs needed, budget needed, and the hours of operation.
We’ll use POISSON.DIST() using the Mean=40. For #1: [specific target], we’ll use probability mass function. For #2: [maximum or <= range], we’ll use cumulative distribution function.
Finally, we’ll visualize it using 2 charts and present the recommendation. Let’s get to work…
We will tabulate the data and calculate the probabilities at each trial using mass and cumulative versions of POISSON distribution. It looks like this:
Then we chart the results for each method which look as follows:
Now we have all the information needed to make a recommendation based on the observation.
– There’s about zero chance of having exactly 20, 22…all the way to 26 dogs (mass). Also zero chance, of having 24 dogs or less.
– About zero chance of having 54 or more.
– About 6.3 % chance of having 40 dogs.
– Almost certainly (99%+ probability) of having 56 dogs or less.
– Small chance of 32 dogs, a little higher chance of having 46 dogs (about 3% vs 3.8%).
Based on these figures, it’s prudent to plan for accommodation of 32 to 46 dogs with room for error and scale.