Poisson Distribution
Answer 7b

It's no damn good.

Explanation

It is obvious that Willi Feller has lived his life in the lap of academe, and never made pin money selling refrigerator cookies to the frozen food man. In the real (or frozen) world, a no-raisin cookie is business suicide, and a 1-raisin cookie is simply ridiculous, and simply ridiculous is just a different form of business suicide. The cookie customer should have a sense of multiple raisins in even the sparsest cookie. What means "multiple?" As any arithmetic teacher will tell you, especially if she is just back from her summer enrichment course, "multiple" means a number that cannot be subitized (its numerosity taken in at a glance, without literal counting). That limit is somewhere around 5. Then the effort should be to guarantee, not that no cookie contains no raisins, but that all cookies contain what the untutored eye will perceive as many raisins, namely: at minimum not less than 5 raisins. Then our task is to see to it that a 4-raisin cookie will not arise more than once in 1,000 cookies. That is, to bring it about that p(4) = 0.0010 or less.

Scanning the Poisson Table with these criteria in mind, we find that our desired rate, among those there given, is r = 15, for which p(4) = 0.0006, rounding up to the desired 0.0010. This is three times more raisins than Feller envisions. Will those who prefer the Feller cookie, please raise your hands?

Exactly.

Comment

Mrs Fields would never have come within a mile of making this insensitive business mistake. See her autobiography.

Late Breaking Cookie News: Evisceration of 12 oatmeal raisin cookies, acquired on 20 Apr 2004 from the local supermarket purely in the name of science, revealed (a) raisin fragments rather than whole raisins, which is another and cheaper form of disperson of raisin content; and (b) a small sample average of about 15 of these raisin presences per cookie. The prosecution rests.

These cookies, it turns out (interview with local supermarket staff, 20 Apr 2004), come to the local bakepoint as refrigerated doughballs, which are flattened and warmed to produce the cookie. No mixing of dough occurs on site, and local personnel are entirely uninformed about the dough process. We suspect that the process, once our undercover agents obtain access to it, will prove to be such as to secure better than Poisson randomness in arranging raisin presences per cookie. If so, this problem ends by vanishing as a Poisson problem. It may suitably endure as the solution of a business problem.

24 Aug 2007 / Contact The Project / Exit to Resources Page