Haha I like your thread's title
Yes it's 0 There's no worry to have about that.It zero, isn't it? If I think about Z=X-E[X], the mean (expectation) of Z is zero (this much is quite straightforward). The only difference between my Z and the Y in the problem statement is that Y is scaled by the standard deviation. I think E[Y]=0. Still, feel free to confirm this or shoot it down like a lame duck.
But where the standard deviation of X intervenes it's in the variance of Y.
Indeed, recall that , where a is a constant, and that , again where a is a constant.
So here, we'd have
It helps transforming a normal distribution into a standard normal distribution (have a look here : Normal distribution - Wikipedia, the free encyclopedia ). It's useful because we know the centiles of the standard normal distribution (there are tables called "z-tables"), but there is no table giving directly the centiles of a normal distribution in general.I found that expression used several times in a few different spots in my text. It seems like an important proportion, but there is no discussion nor even explicit mention of it solo. Maybe if someone could just explain what that proportion is briefly, the lights might come on for me...