VCE Methods Question Thread!

[Adammurad]

A manufacturer finds that, in the long run, 10 per cent of the manufactured
articles are defective. If a sample of 10 articles is randomly selected,
calculate the probability that:
(a) The sample contains exactly two defective articles
(b) The first two articles inspected are defective and the remainder are not
defective
(c) The sample contains more than one defective article.
Can anyone help with working out and a solution thanks

[keltingmeith]

Hi,
For Q10c) http://imgur.com/a/oAFBd

I don't entirely agree with the answer's working but I might be wrong. Although we need 4 standard bottles (ie random variable X), however we can't write it as 4X, it must be X+X+X+X? We can't sum random variables like they have. Same with Y.

This would lead to a difference variance than what they have. Am I missing something?

Thanks

I completely agree, I reckon the textbook has done this the wrong way. You will definitely get a different variance if you did it your way - and I honestly don't know what to tell you, other than ignore them and trust yourself.

Hey, could someone help me with both questions

http://imgur.com/a/uDNKG

thanks

I can think of several ways to do this, but need information from the previous parts to know for sure. Can you sure those parts, and maybe tell us what methods you have tried to solve it so we can let you know why they may not work?

A manufacturer finds that, in the long run, 10 per cent of the manufactured
articles are defective. If a sample of 10 articles is randomly selected,
calculate the probability that:
(a) The sample contains exactly two defective articles
(b) The first two articles inspected are defective and the remainder are not
defective
(c) The sample contains more than one defective article.
Can anyone help with working out and a solution thanks

This question is actually quite nice if you can figure out a few little tricks! Firstly, can you think of any probability distribution that can describe this situation?

[Adammurad]

Do you have a link into where this question is from?

[undefined]

I can think of several ways to do this, but need information from the previous parts to know for sure. Can you sure those parts, and maybe tell us what methods you have tried to solve it so we can let you know why they may not work?

http://imgur.com/a/uDNKG

so I've tried using tan inverse to find theta, but to do this i need to alter the length of the adjacent side to make a right angled triangle. as seen in the picture, the hypotenuse doesn't actually touch the x-axis. also, for the next question i need the angle for the first one to answer.

[keltingmeith]

Do you have a link into where this question is from?

... No? You posted it?

http://imgur.com/a/uDNKG

so I've tried using tan inverse to find theta, but to do this i need to alter the length of the adjacent side to make a right angled triangle. as seen in the picture, the hypotenuse doesn't actually touch the x-axis. also, for the next question i need the angle for the first one to answer.

Thanks for the link! Turns out I was thinking of things the wrong way round, but I definitely needed the link to know that for sure.

So, at rest (theta=0), the pendulum has distance of d=0. This means that the straight line up of 24.8cm is also the length of the pendulum. Next, assume the base is the furthest horizontally that the pendulum can move (implied by the question), and so the length between the center to the end of the pendulum is 3cm. Can you start to see a triangle forming now that you can use?

[Bri MT]

Hey, could someone help me with both questions

http://imgur.com/a/uDNKG

thanks

I think that the length of the pendulumn arm is 24.8cm. Using this, and 3cm. Try using sin inverse rather than tan inverse.
The second part should be relatively easy once you have the angle, so try it first and if you have difficulties let us know

[Mapleflame]

hey guys- looking for an answer as soon as possible please
If you have G(h) and h(x), how do you find G in regards to x? Is G(h) the same as G( h(x) )?

[keltingmeith]

hey guys- looking for an answer as soon as possible please
If you have G(h) and h(x), how do you find G in regards to x? Is G(h) the same as G( h(x) )?

Yup - it's what we call compounding functions. Feel free to give it a search, there's lots of information on the web about it.

[Mapleflame]

Yup - it's what we call compounding functions. Feel free to give it a search, there's lots of information on the web about it.

so G(h) is the same as G(h(x))?

[keltingmeith]

so G(h) is the same as G(h(x))?

Yup - it's what we call compounding functions.

[Bri MT]

so G(h) is the same as G(h(x))?

Yes, but also note that related rates are no longer explicitly part of the study design,

[Syndicate]

so G(h) is the same as G(h(x))?

You would be better off writing G(h(x)) than G(h) imo.

[undefined]

... No? You posted it?

Thanks for the link! Turns out I was thinking of things the wrong way round, but I definitely needed the link to know that for sure.

So, at rest (theta=0), the pendulum has distance of d=0. This means that the straight line up of 24.8cm is also the length of the pendulum. Next, assume the base is the furthest horizontally that the pendulum can move (implied by the question), and so the length between the center to the end of the pendulum is 3cm. Can you start to see a triangle forming now that you can use?

I think that the length of the pendulumn arm is 24.8cm. Using this, and 3cm. Try using sin inverse rather than tan inverse.
The second part should be relatively easy once you have the angle, so try it first and if you have difficulties let us know

Thanks all for the help, I understand it now.

I also have another question, how would you find the general solution for tanx= -3/sqrt3 ? thanks !

[keltingmeith]

Thanks all for the help, I understand it now.

I also have another question, how would you find the general solution for tanx= -3/sqrt3 ? thanks !

Rationalise the denominator, then I think you'll find it turns into something you've seen before.

[Lavar Big BBB Balls]

Hi

For part c, calculating the variance, here http://imgur.com/a/Rx2WE

Why is my method wrong? The correct answer is 400 but the answer made it in terms of the random variable X before evaluating