VCE Methods Question Thread!

[knightrider]

no difference numerically, you can think of it in terms of areas and hopefully see it with just a little geometric intuition:

what's the difference between the areas that those two probabilities describe, given a probability density function? you find the area between -2 and 5 including those points, or excluding them, it should make zero distance(i think you meant difference) because whether you include the line on the end or not wont change the area because an infinitely thin line has an area of zero. So by taking away the edges and using < instead of <=, you're taking away zero area and therefore not changing the probability

Thanks silverpixeli 

so you wouldn't lose marks for writing the probabilities either way right ?

[silverpixeli]

Thanks silverpixeli 

so you wouldn't lose marks for writing the probabilities either way right ?

correct, they're both the same from a maths perspective (just in the case of continuous random variables, it DOES MATTER in the discrete case because individual values can make a big difference if they are included/not)

[knightrider]

correct, they're both the same from a maths perspective (just in the case of continuous random variables, it DOES MATTER in the discrete case because individual values can make a big difference if they are included/not)

thanks silverpixeli 

[knightrider]

For this statement

is this equivalent to

OR

[keltingmeith]

For this statement

is this equivalent to

OR

Yes.

[knightrider]

Say if you have

to find the standard deviation you would do

why don't we do to find the standard deviation?

[silverpixeli]

Say if you have

to find the standard deviation you would do

why don't we do to find the standard deviation?

standard deviation is just defined as the positive square root of the variance, so we take the positive one by convention

[knightrider]

standard deviation is just defined as the positive square root of the variance, so we take the positive one by convention

Thanks silverpixeli 

[StupidProdigy]

percentages, just like probabilities, will be given by areas (0.5 area under the pdf means 50% of the values are in that region, just like it would mean you have a 50% chance of getting a value in that region if you were talking about a random experiment)

This isn't one we can do by hand, you should have a function on your calculator for it. ti-nspire has a function to calculate the area between x=30 and x=33 on a normal curve with that mean and standard deviation. not sure about classpad/other calculators, but its definitely a CAS question

Why is it that you can't use the 68-95-99.7% rule here? thanks

[silverpixeli]

Why is it that you can't use the 68-95-99.7% rule here? thanks

Good pickup, 30-33 corresponds to 2-3 standard deviations above the mean for this distribution. but the rule is approximate, not exact,  so unless they asked you to do it like 'using the 68-95-99.7 rule, find an approximate value for the ...' you could get a more accurate answer (more decimal places) if you found the area with a CAS. Or, if it came up on a tech free, the rule is all you would have so you'd have to go with that.

Personally (can't guarantee this is the way with the VCAA) though, I think you're better off going to the CAS when you have it to get a little more accurate of an answer

[StupidProdigy]

Good pickup, 30-33 corresponds to 2-3 standard deviations above the mean for this distribution. but the rule is approximate, not exact,  so unless they asked you to do it like 'using the 68-95-99.7 rule, find an approximate value for the ...' you could get a more accurate answer (more decimal places) if you found the area with a CAS. Or, if it came up on a tech free, the rule is all you would have so you'd have to go with that.

Personally (can't guarantee this is the way with the VCAA) though, I think you're better off going to the CAS when you have it to get a little more accurate of an answer

Thanks Silverpixeli, I just was unsure when it was appropriate to use the rule or not and forgot it wasn't exact, but your response has clarified this! Cheers

[knightrider]

For this question.

If X is normally distributed with μ = 40 and σ = 7, find, correct to 4 decimal places:

 Pr(X ≥ 30) and Pr(25 ≤ X ≤ 45).

i got Pr(X ≥ 30)=0.9234 and Pr(25 ≤ X ≤ 45)=0.7464

Are my answers right?

[Apink!]

Hi for this question,
Could someone please confirm that I am right? (no answers)

Farmer Taylor of Burra has two tanks.  Water from the roof of his farmhouse is collected in a 100kL tank and water from the roof of his barn is collected in a 25kL tank.  The collecting area of his farmhouse roof is 200 square metres, while that of his barn is 80 square metres.  Currently, there are 35kL in the farmhouse tank and 13kL in the barn tank.
Rain is forecast and he wants to collect as much water as possible.  He should:
(A) empty the barn tank into the farmhouse tank
(B) fill the barn tank from the farmhouse tank
(C) pump 10kL from the farmhouse tank into the barn tank
(D) pump 10kL from the barn tank into the farmhouse tank
(E) do nothing.


I got A. Anyone else get it as well?

[knightrider]

How would you do this question attached ?

where

[@#035;3]

Hey guys, quick few questions; thanks in advance

1) If a coin is tossed three times and it is known that at least one toss resulted in a tail, find the probability that there will be
one tail.

2) A target consists of four coloured concentric circles with radii r cm, 2r cm, 3r cm, 4r cm respectively. Assuming that anarcher hits the target every time and that they are equally likely to hit any point on the target, what is the probability that the arrow hits: 
a) the bullseye
b) The region between the circles with radii 3r cm and 4r cm?
c) The bullseye and the region between the cirlces with radii 3r cm and 4r cm


It'd be very appreciated if anyone could help, cheers.