VCE Methods Question Thread!

[Orb]

need some help please!

Which past paper was this off? It seems weirdly made..

[qwerty101]

Which past paper was this off? It seems weirdly made..

It's E, off a VCAA paper, ended up getting it couple of minutes after posting it. just use the independent rule and divide by Pr(Q) and simplify.!!

[AndyCau]

am i meant to use the inv norm cdf here? just unsure how to figure out the area of the curve first if thats what im meant to do

[StupidProdigy]

Anyone have some links to info about graphs to raised to non integer powers (eg x^(1/3))?

[keltingmeith]

Anyone have some links to info about graphs to raised to non integer powers (eg x^(1/3))?

http://atarnotes.com/pages/?p=notes&a=feedback&id=1741

[Splash-Tackle-Flail]

When writing down the mean, or median, or variance, or standard deviation, do we need to include units? e.g. variance=5cm if the distribution is the hight of a bunch of kids.

[Splash-Tackle-Flail]

Is the 68% 95% 99.7% rule only approximations? or is the middle 95% of the distrubution exactly within two standard deviations from the mean?

[StupidProdigy]

When writing down the mean, or median, or variance, or standard deviation, do we need to include units? e.g. variance=5cm if the distribution is the hight of a bunch of kids.

Yeah it's a good idea to do that in order to properly answer the question. Don't use it for variance though because that still has the squared values.

Is the 68% 95% 99.7% rule only approximations? or is the middle 95% of the distrubution exactly within two standard deviations from the mean?

Just an approximation. Try typing into cas 'normcdf(-1,1,0,1)'. It gives the result ~0.682689 (not 0.68 exactly) which obivously represents the probability within one standard deviation either side of the mean.
Hope that's all clear

[Splash-Tackle-Flail]

Yeah it's a good idea to do that in order to properly answer the question. Don't use it for variance though because that still has the squared values. Just an approximation. Try typing into cas 'normcdf(-1,1,0,1)'. It gives the result ~0.682689 (not 0.68 exactly) which obivously represents the probability within one standard deviation either side of the mean.
Hope that's all clear

Thanks, yep, very clear- aaand I got another one

Mr Lim, a physics teacher, sets a particularly hard test for his students. I finds the average mark is 54 and the standard deviation is 8. He decides to award the top 10% an A, and fail the bottom 10%. Find, correct to the nearest whole number:
the lowest mark required to achieve an A.

So I just did the usual find the z score that correlates to the bottom 90%, then found the actual mark required using the rule, which was 64.25 to two decimal places. However this is saying that the lowest mark required to get an A is 64.25, which means if we have to round to the nearest whole number, would be round up or down? My problem is that if we round down (which is closer), we get a value of 64, but if a student gets a mark of 64, then technically they haven't scored in the top 10% and shouldn't get an A. So I rounded up instead to 65, but BOB says 64..

So the question is, what would you do in these sorts of situations- I kinda saw it like one of those "break-even" questions in Further, but would be good to confirm which answer is correct!

[Floatzel98]

Show that if X is a random variable with mean and variance , and , then and .

I don't really know how to go about the question. Any tips?

[Splash-Tackle-Flail]

Show that if X is a random variable with mean and variance , and , then and .

I don't really know how to go about the question. Any tips?

Ooooh This one looks really cool!
First, showing


Now,
Edit: epiphany for second part;easier way to prove

[Floatzel98]

Ooooh This one looks really cool!
First, showing


Now,
Edit: epiphany for second part;easier way to prove

Damn you make it look so easy. I mean the steps are simple once you know what to do, but actually finding out what to do is the hard part. Thanks a bunch man!

[Floatzel98]

I was looking at pi's probability notation guide in the resources, but I'm still a bit confused to how we show our workings on paper for Binomial and Normal Distribution questions.

Spoiler

The range of scores on a particular test are such that they hold a mean of 60 with a standard deviation of 4.

NORMAL CDF
a) Find the probability of a student's scores lie between 55 and 62

On the TI-Nspire;
On the classpad;

On paper:
Let X be the range of scores of students on the test.

With this one for example, why do we write ? Where does the 16 come from exactly? For ND questions still, does it matter if we use the this notation or do we always have to write out the full integral to be correct?

[Orb]

Thanks, yep, very clear- aaand I got another one

Mr Lim, a physics teacher, sets a particularly hard test for his students. I finds the average mark is 54 and the standard deviation is 8. He decides to award the top 10% an A, and fail the bottom 10%. Find, correct to the nearest whole number:
the lowest mark required to achieve an A.

So I just did the usual find the z score that correlates to the bottom 90%, then found the actual mark required using the rule, which was 64.25 to two decimal places. However this is saying that the lowest mark required to get an A is 64.25, which means if we have to round to the nearest whole number, would be round up or down? My problem is that if we round down (which is closer), we get a value of 64, but if a student gets a mark of 64, then technically they haven't scored in the top 10% and shouldn't get an A. So I rounded up instead to 65, but BOB says 64..

So the question is, what would you do in these sorts of situations- I kinda saw it like one of those "break-even" questions in Further, but would be good to confirm which answer is correct!

The correct answer should be 65 and that's the way VCAA would rule it, but for peace of mind, if this was set as a question on the actual methods exam, VCAA wouldn't ask you to round, they'd ask for an exact answer.

And yes, I clarified it with one of the teachers on the exam panel, so a.k.a a question that asks you to round like this won't be on the final

@floatzel

The 60 is equivalent to the mean, and the 16 is the variance. They tell us the standard deviation is 4, and the sd is just the square root of the variance , so 4^2 = 16.

For normal distrib questions, you can use this notation and it should be fine. As always, look at the number of marks that they allocate. If it's 2 or less then you'll be fine. If it's 3+, then some other working should be shown.

[Splash-Tackle-Flail]

The correct answer should be 65 and that's the way VCAA would rule it, but for peace of mind, if this was set as a question on the actual methods exam, VCAA wouldn't ask you to round, they'd ask for an exact answer.

And yes, I clarified it with one of the teachers on the exam panel, so a.k.a a question that asks you to round like this won't be on the final

Ah thanks!