I realised today I’ve been advising my students… not wrong, exactly, but imprecisely. Capriciously. Unmathematically. Even through it was in statistics, where such things are usually tolerated, I felt it was worth putting it right.
It was in a scenario such as this:
The times an athlete takes to run 200m are assumed to follow a normal distribution with a mean of 22s and a standard deviation of 0.4s. What is the probability of the athlete running 200m in less than 21s?
In the olden days, before the Classwiz was pretty-much-mandatory, the method was always:
That’s not too bad, but the calculator makes it better.
My up-to-today approach on the Classwiz would have been:
But that ‘a big negative number’ bugs me. What if it’s the wrong big number? Minus a billion will usually work, but what if mu is big and negative, or is sigma is large?
In practical terms, doing it ‘right’ will make no difference at all - the imprecisions in the model will usually dwarf the tiny difference it makes.
But, it removes a bit of arbitrariness that was bugging me. And while I’m hiding the fact that I’m using a calculator from the Mathematical Ninja, I’m sure they’d approve.