VCE Methods Question Thread!

[knightrider]

A little tip, always take notice of questions which give you two sets of values or bits of info because they often require simultaneous equations to be solved!
So the mean is calculated by n*p and variance is n*p*q or the more useful n*p*(1-p)
np=20
np(1-p)=14
Solve simultaneously for p

Thanks StupidProdigy 

[knightrider]

How would you guys go about sketching this function.

How do you know where the asymptotes are when it has been translated?

[IntelxD]

How would you guys go about sketching this function.

How do you know where the asymptotes are when it has been translated?

tan(x)=sin(x)/cos(x). Thus, we have asymptotes when cos(x) = 0. Due to the dilations/translations for the given function, you will have to solve cos(0.5(x-pi/4))=0 to find the asymptotes. Try that out.

Thanks so much cosine 

the answer says though?Is this wrong?

The answer 2sin(2k) is correct. The extra working after obtaining dy/dx=2sin(2x) is unnecessary. All you need to do is sub in x=k.

[knightrider]

tan(x)=sin(x)/cos(x). Thus, we have asymptotes when cos(x) = 0. Due to the dilations/translations for the given function, you will have to solve cos(0.5(x-pi/4))=0 to find the asymptotes. Try that out.

The answer 2sin(2k) is correct. The extra working after obtaining dy/dx=2sin(2x) is unnecessary. All you need to do is sub in x=k.

Thanks IntelxD 

[Apink!]

Could someone please explain how I can approach questions like this?:

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 is?

Help

[knightrider]

How would you do this question? (attached)

[keltingmeith]

How would you do this question? (attached)

You might find it easier if you convert to the Z score.

[Floatzel98]

I'm getting a bit confused on how to do questions like this:

A fair die is rolled 50 times. Find the probability of observing: a) no more than 10 sixes b) at least 10 sixes.

Find the probability of getting at least nine successes in 100 trials for which the probability of success is p = 0.1.

A fair coin is tossed 50 times. If X is the number of heads observed, find a) Pr( X = 25) b) Pr( X =< 25)

I am pretty sure we need a calculator to do these. But the problem is my book has no instructions or examples on how to solve questions like this. I've looked around the forum and other places online but I haven't anything similar yet. I've even checked the worked solutions for these questions but all they have is by using the CAS calculator. if anyone could help that would be great

[warya]

I'm getting a bit confused on how to do questions like this:

A fair die is rolled 50 times. Find the probability of observing: a) no more than 10 sixes b) at least 10 sixes.

Find the probability of getting at least nine successes in 100 trials for which the probability of success is p = 0.1.

A fair coin is tossed 50 times. If X is the number of heads observed, find a) Pr( X = 25) b) Pr( X =< 25)

I am pretty sure we need a calculator to do these. But the problem is my book has no instructions or examples on how to solve questions like this. I've looked around the forum and other places online but I haven't anything similar yet. I've even checked the worked solutions for these questions but all they have is by using the CAS calculator. if anyone could help that would be great

If the answer to part a is 0.7986 I can help, don't want to explain the wrong thing haha

[cosine]

For circular functions, can amplitudes be negative? Because I was doing an IARTV practice exams from 2001 and the possible answers had negative amplitudes... For a case like this, just generally, should we guess our form of the answer but with the incorrect notations? (As opposed to leaving it out or wasting heaps of time on that question). Cheers

[silverpixeli]

I'm getting a bit confused on how to do questions like this:

A fair die is rolled 50 times. Find the probability of observing: a) no more than 10 sixes b) at least 10 sixes.

Find the probability of getting at least nine successes in 100 trials for which the probability of success is p = 0.1.

A fair coin is tossed 50 times. If X is the number of heads observed, find a) Pr( X = 25) b) Pr( X =< 25)

I am pretty sure we need a calculator to do these. But the problem is my book has no instructions or examples on how to solve questions like this. I've looked around the forum and other places online but I haven't anything similar yet. I've even checked the worked solutions for these questions but all they have is by using the CAS calculator. if anyone could help that would be great

the pure, 'tech free' way to do it is to use the binomial formula to find the probabilities like:

X=num sixes from 50 rolls
Pr(no more than 10 sixes) = Pr(X<=10) = Pr(X=0)+Pr(X=1)+...+Pr(X=10)

but obviously this isn't how you want to be doing it, and you're not going to do that for anything other than the simplest examples with really small n, or maybe when you can use a trick
(like say we want Pr(X>1) then that's Pr(X=2)+Pr(X=3)+...+Pr(X=50) but its also 1-Pr(X<=1) = 1-Pr(X=0)-Pr(X=1) which is doable)

Your calculator should have a 'binomialCdf' function (not sure what its called on classpad) that lets you calculate Pr(X=a)+...+Pr(X=b) in one function, rather than lots., you just need a point to start counting and a point to finish counting

For circular functions, can amplitudes be negative? Because I was doing an IARTV practice exams from 2001 and the possible answers had negative amplitudes... For a case like this, just generally, should we guess our form of the answer but with the incorrect notations? (As opposed to leaving it out or wasting heaps of time on that question). Cheers

Amplitude values should always be positive (not sure what else you are asking)

I'm not sure what you're asking

[Floatzel98]

Your calculator should have a 'binomialCdf' function (not sure what its called on classpad) that lets you calculate Pr(X=a)+...+Pr(X=b) in one function, rather than lots., you just need a point to start counting and a point to finish counting

Thank you so much, I knew there was a calculator function for it somewhere I just didn't know what it was. How to you enter values into it? Would the syntax be something like binomialCdf(0, 25, 50, 0.5) if the you wanted Pr(X =< 25) where n = 50 trials and the success probability is 0.5?

Thanks a lot

[silverpixeli]

Thank you so much, I knew there was a calculator function for it somewhere I just didn't know what it was. How to you enter values into it? Would the syntax be something like binomialCdf(0, 25, 50, 0.5) if the you wanted Pr(X =< 25) where n = 50 trials and the success probability is 0.5?

Thanks a lot

something like that! if you access it through the menu on ti-nspire, rather than typing it, (iirc something like menu>5>5>E but you can read the lists) it comes up with an entry window and it asks you for the different values by name (n, p, a, b in whatever order). Most of the probability distribution functions are in this list and have similar input options, that will probably help when you get up to normal distributions (very calculator heavy questions)

[knightrider]

How would you do this question? (attached)

Can anyone help with this question?
Thanks 

[keltingmeith]

Can anyone help with this question?
Thanks 

I did help you with that question - I'd suggest finding the z-score. Also, remember that a normal distribution is symmetrical about the mean - consider drawing the distribution and shade under the curve what each probability is referencing.