I can do it on my calculator (fx100au) not sure if everyone else can. But do you reckon I'll lose any marks for having a more accurate answer compared to the "approximate" answer they wanted?
That was something I was genuinely not aware of. I had to look up the user guide to learn how to do standard normal probabilities on the fx-100AU plus. It looks like the standard normal is the only one it can do.
It also appears that the more classical fx-82AU plus II doesn't have this functionality. Which was probably why I never considered it for the fx-10AU plus - oops.
In theory, I would hope that it doesn't matter. The only thing I'd be worried about in practice is if NESA took that into consideration themselves as well (when writing down their list of approved calculators). If they knew that some calculators had this functionality, then they should know to mark accordingly to it wherever needed. Yet if they
weren't aware, I would really hope they don't deduct marks for "pulling a number out of thin air" when it was just handy calculator knowledge.
That being said, I would hope that they know to actually compute \( P(-1.02\leq Z\leq 1.02)\) on statistical computing software, to check your answers against it. I'd lean towards it should be no problem; just not confident enough to guarantee anything sadly.
I mean, the difference between the two is 1%. It's tiny, minor, basically nothing - you can probably feel pretty safe in that you'll get it accepted.
On this, I'm not a HSC expert, but they should be aware that some of the calculators they allow can calculate z-scores like this, and so should be prepared to get answers like you have given.
But like, do you really call the entire expression \(P(Z\leq z)\) a '\(z\)-score', instead of just the \(z\) bit itself?