Maths Methods 3/4 Help Thread 2011

[nacho]

Extended response chapter 1 pg 54 q6a
how do you figure out the inner x intercepts? The outer two are fairly obvious.. But the inner two?

What book?

sorry, mquest

[david10d]

yo dawgz


A normal random variable has a mean of 8.0 and a Sd of 2.0. Find the probability X < 12 | X> 8

tenk Q

[Andiio]

yo dawgz


A normal random variable has a mean of 8.0 and a Sd of 2.0. Find the probability X < 12 | X> 8

tenk Q

Is the answer just 0.9545?

[thushan]

Yup.

[david10d]

yeah, it's from Kilbaha exam 1

how did you get that answer?

[Andiio]

It'd be kinda hard without a calc to get a precise decimal approximation,

but just use the 68-95-99.7% rule! (It may be easier to see it if you convert to the standard normal dist)

Pr(X<12|X>8 ) = Pr(X<12 intersection X>8 )/Pr(X>8 ) = Pr(8<X<12)/Pr(X>8 ) = (.95/2)/0.5 = 0.95

EDIT: emote fail

[Andiio]

Isn't the domain of f^-1(x) = (0,1/2] and not (0,1/2)?

[nacho]

F(x) = (x-1)^2(x-2) +1
find the real value of p for which f(x) =p has exactly one solution

edit: nvm I got it.. Lol that was dumb. Although could someone adress the question I posted above n the previous post? The question from mathsquest.. Still don get it, despite at how simple it looks

[paulsterio]

you have to graph it, you will see that it has sort of this shape
   
    _        /
   /  \      /
  /    \    /
 /      \_/
/

Basically, you find the co-ordinates of the two turning points, say they turn out to be (a,b) and (c,d) with c being the one on the right
so if p<b or p>d, there will be one solution, as seen from the graph

[nacho]

Follow up question from the cubic I provided before
find the real values of h for which only one of the solutions to the equation f(x+h) =1 is positive.
I think I'm on the right track but obviously missing something crucial as I put h = 2
thanks

[paulsterio]

that's a translation, so you want it somehow so that the bit of the function that lies to the right of the y-axis is only one branch, so referring to the graph before, you have to translate "c" units to the right, because the right TP is (c,d) so h = -c

might not be right, could someone confirm? i don't have a CAS or paper on me atm!

[nacho]

that's a translation, so you want it somehow so that the bit of the function that lies to the right of the y-axis is only one branch, so referring to the graph before, you have to translate "c" units to the right, because the right TP is (c,d) so h = -c

might not be right, could someone confirm? i don't have a CAS or paper on me atm!

yea see that's what I thought but they've said it's [1,2)
edit : I think I misinterpereted what you were trying to say,
however I'm still not sure how to get the answer


another two questions:
someone please explain how to obtain point C
from question 3f of VCAA 2008?

And,
"The minimum number of times that a fair coin can be tossed so that the probability of obtaining a head on each trial is less than 0.0005" ?

[LachieEvans]

that's a translation, so you want it somehow so that the bit of the function that lies to the right of the y-axis is only one branch, so referring to the graph before, you have to translate "c" units to the right, because the right TP is (c,d) so h = -c

might not be right, could someone confirm? i don't have a CAS or paper on me atm!

yea see that's what I thought but they've said it's [1,2)
edit : I think I misinterpereted what you were trying to say,
however I'm still not sure how to get the answer


another two questions:
someone please explain how to obtain point C
from question 3f of VCAA 2008?

And,
"The minimum number of times that a fair coin can be tossed so that the probability of obtaining a head on each trial is less than 0.0005" ?

You can sub it into the binomial distribution where n=x and then solve for n. Or alternatively, and more logically, you can just solve (.5)^n=.0005 and you get 8 or something from memory.

[BlueSky_3]

Bit off topic, but is it true that ~ 84% was required for an A+ on the 2008 methods CAS exam 2 ?

[tony3272]

Yeah thats true. Last year was 82% as well, and 09 was 86%