VCE Methods Question Thread!

[soNasty]

Apologies for the bombardment of questions

The scores, X on an aptitude test are such that X~N(75,35)
Find the interquartile range ie. the middle 50% of scores

I got it!
I just solved for k when pr(z<k)=0.25 and for 0.75 as well and solved for x after subbing into z score formula

[keltingmeith]

I just solved for k when pr(z<k)=0.25 and for 0.75 as well and solved for x after subbing into z score formula

Here's a question if you come back:

You solved for Pr(z<k₁)=0.25 and Pr(z<k₂)=0.75 seperately, yes? What did you notice about the relationship between the two ks?

[soNasty]

Here's a question if you come back:

You solved for Pr(z<k₁)=0.25 and Pr(z<k₂)=0.75 seperately, yes? What did you notice about the relationship between the two ks?

one's negative and one's positive!

[keltingmeith]

one's negative and one's positive!

Brilliant! In fact, due to the symmetry properties of the normal distribution, in general:



#themoreyouknow

[Yacoubb]

The probability of a target shooter hitting the bullseye on any one shot is 0.2.

What is the smallest number of shots the shooter should make to ensure a probability more than 0.95 of hitting the bullseye at least once?

Pr(X≥1) ≥ 0.95
1 - Pr(X≥1) ≥ 0.95
Pr(X<1) ≤ 0.05
0.05 = (0.2)⁰ * (0.ⁿ
n = 13.4

The answer is 14. How do I know when to round up/down? Thanks!

[Conic]

If there are 13 throws, then the probability of hitting at least once is 0.9450, to 4 decimal places. When there are 14 throws the probability is 0.9560, so 14 is the smallest number of shots that fits the requirements. Generally you would round up, but it's best to check of your answer makes sense. You can't have 0.4 of a throw, so for the probability to be high enough you need to have another throw.

[keltingmeith]

If there are 13 throws, then the probability of hitting at least once is 0.9450, to 4 decimal places. When there are 14 throws the probability is 0.9560, so 14 is the smallest number of shots that fits the requirements. Generally you would round up, but it's best to check of your answer makes sense. You can't have 0.4 of a throw, so for the probability to be high enough you need to have another throw.

This - so much this.
The best thing with these questions is to look at what the number represents - it's a measure of throws in this instance, yes? So, when you get 13.4, can you have 0.4 of a throw? If you answered yes, you're absolutely spectacular and must show me this 0.4 of a throw.

So obviously, you have round up or down - this is when you follow through as Conic has described. This is what I like to happily call our bullshit check - make sure you always do a bullshit check after every question. Basically, look at your answer - if it doesn't make sense in the situation you have, it just failed the bullshit check, and you should make a note to come back to the question later.

[Rod]

Hey guys:

find the derivative of: e^2x +2/e^4 -2

My working:

I defined U, U', V and V'

f'(x) = (e^2x-2) (2e^2x) - (e^2x +2)(2^e^2x) all over (e^2x-2)^2

Can I leave my answer to this? Or do I have to simplify it to -8e^2x/(e^2x-2)^2 ?
If so, can you please show me how

thank you

[keltingmeith]

There's no need to define anything - the diff of the first term is 2e^(2x) (chain rule/standard derivative), and the rest are constants, so their derivative is 0. So, the derivative of that expression is 2e^(2x)

[Rod]

There's no need to define anything - the diff of the first term is 2e^(2x) (chain rule/standard derivative), and the rest are constants, so their derivative is 0. So, the derivative of that expression is 2e^(2x)

Oh are you sure ?

The answer was -8e^2x/(e^2x-2)^2

And sorry I meant 'let' not define

[keltingmeith]

I'm positive - if that's the answer, you've given us the wrong function.

[Rod]

I'm positive - if that's the answer, you've given us the wrong function.

Ahh thanks you're right I'm probably wrong. I'll clarify the function tomorrow, going to bed now.

Thanks so much again for the help!

[Phy124]

Hey guys:

find the derivative of: e^2x +2/e^4 -2

My working:

I defined U, U', V and V'

f'(x) = (e^2x-2) (2e^2x) - (e^2x +2)(2^e^2x) all over (e^2x-2)^2

Can I leave my answer to this? Or do I have to simplify it to -8e^2x/(e^2x-2)^2 ?
If so, can you please show me how

thank you

Given the answer you have given I assume you mean

In which case



Because the factorisation of is reasonably easy the simplification is probably necessary. However, should it come up on an exam you can gauge whether it is necessary by how many marks the questions is worth. In regards to SACs it might be best to ask your teacher

Alternatively, an easier way to get the answer is as follows:

[Rod]

Given the answer you have given I assume you mean

In which case



Because the factorisation of is reasonably easy the simplification is probably necessary. However, should it come up on an exam you can gauge whether it is necessary by how many marks the questions is worth. In regards to SACs it might be best to ask your teacher

Alternatively, an easier way to get the answer is as follows:

thanks so much phy

[soNasty]

help!