Poisson Distribution

27. Everybody.

Explanation

From the same column of the Table we used for the previous problem, we see that p(27) = 0.0254, which times 20 rounds up to 1, so that we expect that outcome to occur once in 20 samples. Nothing with more pepperoni in it is likely to turn up in this size sampling of Pete's pizzas.

Comment

Meaning that, once per busload, you are probably going to see a 27-pepperoni pizza.

Now we are going to reflect. Notice that the least paltry pizza in this group of 20 pizzas (it has 27 pieces of pepperoni) has twice the pepperoni of the most paltry pizza (13 pieces). This is a degree of variability that no franchise would long tolerate. There is the bus, parked at Pete's curb, and here are 20 little tykes eating their pizzas, pushing and shoving. Pretty soon they start comparing pepperoni, and someone screams "Hey, he's got twice as much as me," and before you know it, you have a mass pizza fight on your hands. Have you ever cleaned up after a mass pizza fight? Pete should get rid of his machine, cancel his service contract, and rehire the high school kid who used to do the pepperoni. Random has its place; for instances, interviewers need to take random samples of the population. That we know. But pizza should be uniform and dependable, from one kid to the next.

This problem, admittedly, was designed to be silly in order to provide a little comic relief in this otherwise serious lesson. But decisions scarcely less silly are in fact made every day in the business world. That is why so few start-up businesses make it past their first year. Statisticians need to be sensible, and not merely accurate. The highest statistical art is experiment design. A business (with or without random pepperoni) is merely one kind of experiment. Give thought to the design of that experiment.