Yeah another one. If you didn’t see the one I posted an hour or so ago, scroll down. I seem to get blogging ideas in spurts. This one is about our school levy. As you may or may not be aware, the school levy in Madeira failed by 15 votes. (1680-1665 for those of you keeping score at home)
So Carolyn is on the Madeira email list and today she got an email from the Superintendent, mentioning that there were 97 ballots that were not counted (due to problems at the polling places) and 38 provisional ballots (usually people that have recently moved to the district and whose voter records are not updated yet).
The superintendent’s letter said (among other things) that since the final result of the levy was not known, that he is going to hold off on making the $1 million in cuts that they’d have to make if the levy failed, since the outcome is not yet decided.
So, the math/stats geek in me was wondering what the odds were that these 135 ballots would be enough to make up the 15 vote difference. One problem is that there is exactly 1 thing that I remember about my Probability and Statistics classes from college. And that is that when Jay heard that my teacher was “M. Levine”, he unleashed the witty quote (commenting on her age) “She’s 100 if she’s a day”, a quote which has incorporated its way into the Miller family lexicon
Unfortunately, that didn’t help me much in trying to figure out the odds. I thought that it seemed like a binomial distribution. Pascal’s Triangle figured to be heavily involved. My assumption was that there was a 50/50 shot that each vote would be pro or against, and 76 yes votes needed to pass the levy (75 yes would be 60 no and therefore a tie). Essentially it is the same question as if you flip a coin 135 times, what are the odds that 76 or more will be heads?
I used the Excel formula
=BINOMDIST(59,135,0.5,TRUE) (with 59 being 135-76), which comes out to 8.143%
That seemed really low, but upon further review, I believe that to be correct. There was one guy here that I asked that was adamant that the odds were 59/135. I was pretty sure that he was wrong, but he was so adamant that I gave it a second chance, but I am now 99% convinced that he was wrong, and the analysis above is correct.
I emailed a copy of this to the Superintendent too, because I thought he might be interested.