This is the last in our series of 2024 QLD Methods whacks (unless someone flags something else). This one is from the 2024 QLD Methods “Technology-active” Exam. The intended solution can be found in the marking guide (pp 33); the subject report appears to say nothing about the question.
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1) I would suggest QCAA look up the meaning of “suggestion”
2) “Evaluating the reasonableness” of a *prediction* (or forecast or expectation or whatever but NOT “suggestion”) based solely on the actual outcome is nonsense. A prediction turning out wrong (or right) is not enough to tell us whether the prediction itself was reasonable or not.
3) There’s no mention of any time period anywhere. Is the expectation for $1500 in fines per day? week? month? lifetime? Same for the 75 speeds recorded. Or was it just disabled after 75? Why? We also know nothing about how many scooters were expected?
The only correct answer can be that there’s not enough information to say whether the “suggestion” was reasonable or not.
Thanks, James. I have a suggestion: QCAA might stop dressing up their silly questions with idiotic pseudo-modelling flurblegludge.
Marty. I never have worked out your acronyms for the various types of problems in exams and textbooks. Can I suggest IP-MF for this flublegludge. At least then I will feel less ignorant?
“Flurblegludge” (you misspelt it) is not an acronym.
I was not suggesting that “flurblegludge” is itself an acronym 🙂
Ah, ok. What is this Crap Here, and Proof of Stupidity Without Words.
There is no clear dividing line, but the idea is that a WitCH may require some thought to determine the crap, whereas a PoSWW is supposed to be so obvious that one should simply stare in disbelief.
In the end, one should stare at all of it in disbelief. These exams, in part and in sum, are so far from good, sane examination of solid mathematics, the critiquing of individual questions is distracting from the systemic crime.
The intended method is straightforward. However, let me offer a few other comments.
I do not like the conclusion in the marking guide: “The expected total fines is about $1133, which is less than the suggested $1500, so the suggestion is not reasonable.” Why is it not reasonable?
Statistics is a practical subject. However I do not regard this problem as dealing with a practical problem. For example, in practice, how would one know the value of p(10) without already knowing p(x)?
All too often, examiners strive to create problems in probability and statistics so that they will involve some advanced techniques not connected with probability and statistics. In this case, the problem is contrived to involve solving a non-linear equation. The setting of the problem in terms of speeds of e-scooters might be appropriate for assessing students’ knowledge of the Normal distribution; the examiners could set a different problem focussed on assessing the ability of students to solve non-linear equations; e.g. solve for x etc.
I think your comment about knowing
but not knowing the general function 
is a very nice summary of the issue here – the problem is pretending to be something it is not.
Thanks, Terry. Good summary of an atrocious question.
Note that this blogsite assumes that a dollar sign means you are about to insert TeX. You have to write slash-dollarsign to write a dollar sign.
Nit-pick: the parameters of a normal distribution are mean and variance, not mean and standard deviation.
Please explain. I would have thought they are interchangeable.
I think RF’s nitpick is off, but I definitely don’t think of
and 
as “interchangeable”. The fact that schools teach them as interchangeable is an indication of how mathematically shallow is the treatment of this execrable topic.
Please educate this poor soul who has never experienced a statistics lesson in his life. I still would like to learn RF’s definition of parameters of a distribution.
I’ve never had a stats lesson either, but there seem to me some obvious questions, with not difficult answers:
*) What is the benefit and what is the drawback of standard deviation as “parameter”?
*) What is the benefit and what is the drawback of variance as “parameter”?
Of course, given one of the things you can always get the other, by either squaring or rooting. But why choose one as *the* parameter, as the focus? There are obvious arguments but I cannot remember the point ever being made, or even touched upon, in the school setting.
VCAA made a big deal of it a few years ago in an examiners’ report and the latest study design goes so far as to specify that when students write
they are saying 
and should therefore be careful with notation.
My nitpick, if nothing else, is to show that one cannot assume equality of interpretation between states/assessment boards and must therefore be careful. Especially with statistics which seems to be rather poorly understood by said boards and those setting the papers!
Fair enough. Come to think of it, I always use this convention when using the
notation; there is scope for confusion otherwise.
The thing that makes this annoying is that the Nspire CAS has the function
normPdf(x,a,b)wherebis the standard deviation.I’ve seen some teachers use named parameters, i.e. write
to avoid this confusion for their students.
In the books that I have read,
is the most common notation. I have seen 
but it is far less common. This is not confusing until you use numbers instead of symbols and write 
.
However many authors use words. Suppose that
is a random variable with a normal distribution with mean 
and variance 
.