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#### costargh

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##### Methods CAS questions...
« on: November 05, 2007, 03:20:31 pm »
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2 more questions for you math geniuses

Question 1

The .95 quantile for the standard normal probability distribution is approx. equal to
A. -1.960
B. -1.645
C.  0
D.  1.645
E.  1.960

The only thing I can remember about this is [and find in my text book] is the 68-95-98. something rule thingo

Question 2

In the system of equations

x+ay+b=0
2x+cy+d=0

in the variables x and y, where a, b, c and d are real constants has infinitely many solutions, then
A. c=2a and b=d
B. a=c and b=d
C. a=c and b= -d
D. a=2c and b=2d
E. c=2a and d=2b

...Ive got no idea. Simultaneous equations? LOL???

#### melanie.dee

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##### Re: Methods CAS questions...
« Reply #1 on: November 05, 2007, 04:03:07 pm »
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Quote from: "costargh"
2 more questions for you math geniuses

Question 1

The .95 quantile for the standard normal probability distribution is approx. equal to
A. -1.960
B. -1.645
C.  0
D.  1.645
E.  1.960

The only thing I can remember about this is [and find in my text book] is the 68-95-98. something rule thingo

deleted cos it was wroooong haha im an idiot

Quote
Question 2

In the system of equations

x+ay+b=0
2x+cy+d=0

in the variables x and y, where a, b, c and d are real constants has infinitely many solutions, then
A. c=2a and b=d
B. a=c and b=d
C. a=c and b= -d
D. a=2c and b=2d
E. c=2a and d=2b

...Ive got no idea. Simultaneous equations? LOL???

yeh it is simultaneous equations. ok where there is an infinite number of solutions, is where the two simultaneous equations are equal ie they are the same line ultimately

change it to this

x + ay = -b
2x + cy = -d

ok in the first equation its x and the second one 2x. ie a ratio of 1:2. therefore to make the equations the same, you want all the things to be in a ratio of 1:2. so you want

c = 2a and d = 2b

#### melanie.dee

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##### Methods CAS questions...
« Reply #2 on: November 05, 2007, 04:03:56 pm »
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wow i totally got interrupted by a phone call and i thought someone wouldve already posted the answers before me. but nope! yay haha

im not positive about the first one. but lets hope lol

#### costargh

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##### Methods CAS questions...
« Reply #3 on: November 05, 2007, 04:15:38 pm »
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Ahh i see for the second one... but why does that mean there will be infinitely many solutions?

And the first one is wrong. I put E also using the same method you did. The answer is D

#### melanie.dee

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##### Methods CAS questions...
« Reply #4 on: November 05, 2007, 04:20:55 pm »
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ah effing hell haha.. i thought the first one seems to easy to be true.

well if you plug it in your calculator, which i should have done, you get D.

invNorm(.95,0,1) = 1.64485

but i dont know why

haha

----------------

for number 2. um it means there are an infinite number of solutions becaause they are the same line and therefore there are solutions all the way up and down that line.. ie every point on that line

edit: oh fuck i know why im an idiot!!

the way i did it assumes doesnt work. because that would assume you're taking the middle area with sd x 2 on either side.

but the question actually asks for neg infinity to some value. not the middle section.

therefore you need to use the calc inverse norm button

#### costargh

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##### Methods CAS questions...
« Reply #5 on: November 05, 2007, 04:22:02 pm »
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Its an exam 1 question... LOL

But still... what the hell did you just plug into your calc? I've never seen that before. Well I've seen it but I dont know what it does =S

#### melanie.dee

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##### Methods CAS questions...
« Reply #6 on: November 05, 2007, 04:30:33 pm »
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how can it be exam one, its a multi choice? plus i dont see how you could do it, unless you had cumulative normal dist table.. which you dont anymore

um in the calc go to catalog, F3, go down to InvNorm, select that, then put in the probability so .95, then the mean, then the SD.

so InvNorm(.95,0,1)

that gives you the value

#### melanie.dee

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##### Methods CAS questions...
« Reply #7 on: November 05, 2007, 04:37:00 pm »
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is this from an old exam maybe, where they didnt have the non calc and non notes exam? and where they used to give you cnd tables? cos i dont see how else you could do that, but someone might prove me wrong

#### cara.mel

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##### Methods CAS questions...
« Reply #8 on: November 05, 2007, 05:44:28 pm »
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Quote from: "melanie.dee"
is this from an old exam maybe, where they didnt have the non calc and non notes exam? and where they used to give you cnd tables? cos i dont see how else you could do that, but someone might prove me wrong

I agree, it can't be exam 1, your exam 1 is exactly the same as normal methods (Which means for probability questions where you could solve it with a matrix, unless you own at matrices by hand draw a tree diagram)

I can't do these questions any more xD, like I have a rough idea of what to do but thats all.

#### Freitag

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##### Methods CAS questions...
« Reply #9 on: November 05, 2007, 05:45:12 pm »
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It's a calculator assisted paper. I did it not long ago.

The second question refers to a matrix and it's determinant not equaling 0.
rediction of Scores:

English: 40 (hopefully) ; Spec: 40, Methods: 40-45, Physics 35, Enhancement: HD. Last year- History 38; I.T 42.

Hopeful ENTER 98. (I need it for my scholarship )

#### melanie.dee

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##### Methods CAS questions...
« Reply #10 on: November 05, 2007, 05:51:18 pm »
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gar i suck at matrices, i have no idea what to do with them haha.

you can still work out the second question according to my method though right?

#### costargh

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##### Methods CAS questions...
« Reply #11 on: November 05, 2007, 06:38:14 pm »
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Yep sorry I should have been more clear lol
VCAA 2005 CAS paper which used to allow notes and calc PLUS had a norm distribution cdf table @ the back. LOL

ARGH I just did exam 2 for the VCAA 2005 CAS paper and got a 30/55!!! THAT IS FREEKIN MADDDDDDDDD.... for me which pips me into the 'B' section for that grade distribution

wowwwwwwww im soo happy. I've found motivation . thats 4 exams down in 2 days. now i have to do some more and be ready for this mo-fo

#### gangreen

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##### Re: Methods CAS questions...
« Reply #12 on: November 05, 2007, 11:09:54 pm »
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Quote from: "costargh"

The .95 quantile for the standard normal probability distribution is approx. equal to
A. -1.960
B. -1.645
C.  0
D.  1.645
E.  1.960

its an inverse probability i think, i remember doing the same question in the 2004 pilot or something.
you say pr(x<c1)=.95 and then inverse it, so you do need a calculator

#### costargh

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##### Methods CAS questions...
« Reply #13 on: November 06, 2007, 04:06:25 pm »
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whats an inverse probability?

#### Galelleo

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##### Methods CAS questions...
« Reply #14 on: November 06, 2007, 04:31:18 pm »
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I think probability of it not happening
but you need mutually exclusive events?
Light a man a fire and he will be warm for the rest of the night.
Light a man ON fire and he will be warm for the rest of his life.