VCE Methods Question Thread!

[gnaf]

So Pr(p hat=1/3) is basically asking for the probability of picking only one red fish in the sample of eight, which just uses combinatorics. In the answers the numerator is the number of combinations with one red and two gold fish and the denominator is the total number of possible combinations.
And to get Pr(p hat> 1/4) there needs to be at least 1 red fish since there are only three fish. Then the Pr(p hat>1/4) = 1-Pr(p hat=0) = 1-(8/16)*(7/15)*(6/14)

Sorry if my explanation is ambiguous, I'm not really sure how to do the formatting for maths questions on atarnotes yet

Thanks so much Eric, so kind of you

When you say "In the answers the numerator is the number of combinations with one red and two gold fish and the denominator is the total number of possible combinations.", where does (8 1) and (8 2) come from (in the answers)?

Can a be lesser than or equal to 2? Or does it have to be less than 2?

[VanillaRice]

Thanks so much Eric, so kind of you

When you say "In the answers the numerator is the number of combinations with one red and two gold fish and the denominator is the total number of possible combinations.", where does (8 1) and (8 2) come from (in the answers)?

Can a be lesser than or equal to 2? Or does it have to be less than 2?

1) The combination we want is 1 red fish and 2 gold fish. (8 1) tells us we want 1 red fish, out of the total number of 8 red fish. More specifically, if we had 8 red fish, (8 1) tells us the number of possible ways we can select 1 fish from this population.
Similarly, (8 2) tells us we want 2 gold fish out of the possible 8.

2) We want to calculate a value for a such that the integral with be equal to 1 (since the total area under a density function is 1). If you substitute a=2, you'll find that the integral will not be equal to 1.

Hope this helps 

[Lavar Big BBB Balls]

Hi,

For Q9 https://m.imgur.com/a/2dANY

I'm stuck on what to do because I'm left with 2 unknowns, instead of just the mean, however I'm confident I have understood the question correctly. The correct answer is 1004ml.

Thanks

[VanillaRice]

Hi,

For Q9 https://m.imgur.com/a/2dANY

I'm stuck on what to do because I'm left with 2 unknowns, instead of just the mean, however I'm confident I have understood the question correctly. The correct answer is 1004ml.

Thanks

We need to use the standard normal distribution.
Using the formula for standardisation

Spoiler

From the question, we can establish

We need to find the z-score - using the inverse normal function on your calculator, we find

Substituting into the standardization formula

You should get mu = 1003.13mL. However, note the question requires us to round to the nearest mL. If we round to 1003mL and solve for Pr(X<998) using your calc, you will get an answer that is >0.02. So, we need to round up to 1004mL. You can check that Pr(X<998)<0.02.
Hope that makes sense 

[Lavar Big BBB Balls]

^ Thanks!!

[Lavar Big BBB Balls]

Soz, another q.


For this q http://imgur.com/a/ATRxu

Q7a) I'm not getting the correct answer which is 0.7834 but I don't see an error in my working.

I still managed to get b correct which is weird because it was dependent on the working done in part a..

Thanks

[Shadowxo]

Soz, another q.


For this q http://imgur.com/a/ATRxu

Q7a) I'm not getting the correct answer which is 0.7834 but I don't see an error in my working.

I still managed to get b correct which is weird because it was dependent on the working done in part a..

Thanks

Hi
Your thinking is right you just made a few algebra mistakes

You just put in some of the numbers wrong

[Lavar Big BBB Balls]

Thanks!!

[TheCommando]

No idea how to do e don't understand it at all (solutions written)
http://imgur.com/a/KuYdH

[Shadowxo]

No idea how to do e don't understand it at all (solutions written)
http://imgur.com/a/KuYdH

From what I can see (image is a bit fuzzy), in d) you determined the time in terms of L. You should be able to just rearrange that equation to get L in terms of t

[simrat99]

Hi,
Can someone please help with the following question?
A real-estate firm owns the Shantytown Apartments, consisting of 7070 garden-type apartments. The firm can find a tenant for all the apartments at $500$500 each per month. However, for every $20$20 per month increase, there will be two vacancies with no possibility of filling them. What price per apartment will maximise monthly revenue? (Use a continuous function to model this discrete situation.)
Thanks!

[keltingmeith]

Hi,
Can someone please help with the following question?
A real-estate firm owns the Shantytown Apartments, consisting of 7070 garden-type apartments. The firm can find a tenant for all the apartments at $500$500 each per month. However, for every $20$20 per month increase, there will be two vacancies with no possibility of filling them. What price per apartment will maximise monthly revenue? (Use a continuous function to model this discrete situation.)
Thanks!

That's an interesting one. The first thing you need to do is decide what kind of a model would be a good fit (eg, sin(x), straight line, quadratic, etc.), and then put it in general form and try to find the unknown parts of it. Things might start making a lot more sense if you actually label some variables, too. (eg, make y=amount people pay individually, x=time in months. Not saying this will work, just something you can try)

Let us know how you go trying that, we might be able to point out where your thinking is going astray.

[Shadowxo]

Hi,
Can someone please help with the following question?
A real-estate firm owns the Shantytown Apartments, consisting of 7070 garden-type apartments. The firm can find a tenant for all the apartments at $500$500 each per month. However, for every $20$20 per month increase, there will be two vacancies with no possibility of filling them. What price per apartment will maximise monthly revenue? (Use a continuous function to model this discrete situation.)
Thanks!

The revenue is amount per month x number of tenants
You know each time you increase the rent by $20 you get 2 less tenants. So, you should be able to model it using this information.
Amount of money per month per apartment = $500 + amount you increase it
Number of tenants = initial number (7070) - amount that leave
Answer below if you're still stuck

Spoiler

Revenue = Amount per month * tenants
= (500+20n)(7070-2n)

[Lavar Big BBB Balls]

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

[undefined]

Hey, could someone help me with both questions

http://imgur.com/a/uDNKG

thanks