Mathematics: Post your doubts here!

[afshinsalim]

Can sum1 plz help me with this question. Its a question from sampling and estimation A2 stats.

A survey was undertaken of the use of internet by residents in a large city. In a random sample of 150 residents, 49 logged on to the internet at least once a day.
i) Calculate an approximate 90% confidence interval for p, the proportion of residents in the city that log on to the internet at least once a day.
ii) A total of 100 similar surveys are carried out and the 90% confidence interval calculated for each survey. State the expected number of intervals that include p.\

I answered (i) but i need help with (ii) please.

 

[Talha Irfan]

please help me with these questions http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s11_qp_61.pdf Q3
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_63.pdf Q2ii

P(X = 0) = 1/10 (given)
remaining integers are 7 from the set and the probability is to be divided equally among them
so the probability of one of the remaining 7 integers = 1 - (1/10) divided by 7 = (9/10) / 7 = 9/70

i) P(X<2) = P(X = - 2) + P(X = - 1) + P(X = 0) + P(X=1)
= 9/70 + 9/70 + 1/10 + 9/70 = 0.486

ii) the probability distribution table looks like

x - 2 - 1 0 1 2 3 4 5
p(X=x) 9/70 9/70 1/10 9/70 9/70 9/70 9/70 9/70

now calculate the variance using the formula
E(X^2) - ((E(X))^2

iii) we are going from the negative of a positive number to its twice. so let's check the possibility of a number existing in negative which is - 2 or - 1
so now first possibility
let a be 1 so probabilities should be added from - 1 to 2(1) = 2

P(X=-1) + P(X=0) + P(X=1) + P(X=2)
= 9/70 + 1/10 + 9/70 + 9/70 = 17/35 (shown)

 

[abruzzi]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s11_qp_33.pdf
Could anyone please help me with question no. 8(ii)? I just can't solve it

Thanks

 

[rawaaaan]

http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_w12_qp_61.pdf
please explain question 1

 

[rawaaaan]

I expanded Σ(x-36)^2 it to pull out the term Σx^2. That is what we are supposed to find.

Consider this example:

(a+b)^2 = 4
a^2 + 2ab + b^2 = 4

If we are given 'ab' and 'b^2', we can easily find a^2 by putting the values into the equation. My solution is exactly the same. Did you get it now?

CAN U PLZ EXPLAIN THE PART AFTER THIS ,HOW WE GOT 27011.76 (27000)

 

[Faaiz Haque]

http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s03_qp_1.pdf
Question 1.
What's the method? I know the formula, how do we get the coefficient for 1/x
Help please. Thanks

 

[rawaaaan]

ii) Probability of length less than 73 m and length greater than 77 m is the same since they are the same distance from mean. A normal distribution curve is symmetric about its mean.
P(X<73) = P(X>77) = 0.15

Let X represent the number of rolls having length greater than 77 m.
n = 8
p = 0.15
q = 0.85

P(X<3) = P(X = 0) + P(X = 1) + P(X = 2)
P(X<3) = (8C0) (0.85)^8 + (8C1) (0.15)(0.85)^7 + (8C2) (0.15)²(0.85)^6
P(X<3) = 0.895

CAN U PLZ EXPLAIN PART I

 

[ZaqZainab]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s03_qp_1.pdf
Question 1.
What's the method? I know the formula, how do we get the coefficient for 1/x
Help please. Thanks

You use the formula and you will get some terms
like x^5,x^4,x^3.........
you will also get a x^-1 term as you say you know the formula you might also know how to apply it
Therm Multiplying with x^-1 will be the coefficient
If you don't get this i can expand it for you and show you

 

[Faaiz Haque]

You use the formula and you will get some terms
like x^5,x^4,x^3.........
you will also get a x^-1 term as you say you know the formula you might also know how to apply it
Therm Multiplying with x^-1 will be the coefficient
If you don't get this i can expand it for you and show you

That makes sense. I did it but my answer is coming as +40. Mark scheme says -40, can you tell me where I went wrong?
4th term : 5C3 *(2x)^2 * (-1/x)^3
= 10 * 4x^2 *-1/x^3
= 40x^2 * -1/x^3
= x ( 40 *-1/x)

 

[ShreeyaBeatz]

how to find the roots. I have pasted question for your easiness
Please help

 

[syed1995]

how to find the roots. I have pasted question for your easiness
Please help

I would like to know the answer to this as well.. How many marks is it worth and which year/paper mate?

 

[sitooon]

X and Y are related by x^n y = c
When we form equation it should be : nlogx +logy = logc

But in marking scheme they use (( ln )) instead of log ! how comes ?

 

[syed1995]

X and Y are related by x^n y = c
When we form equation it should be : nlogx +logy = logc

But in marking scheme they use (( ln )) instead of log ! how comes ?

doesn't matter whether you use log or ln.. you will get the same answer in the end as only the base is changed in one it's e and other 10... However it is preferred to use ln instead of lg because of presence of e(exponential) in some questions which can easily be resolved with ln.

 

[Faaiz Haque]

http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s04_qp_1.pdf

Question 9 ii and iii. With explanation please

 

[ZaqZainab]

That makes sense. I did it but my answer is coming as +40. Mark scheme says -40, can you tell me where I went wrong?
4th term : 5C3 *(2x)^2 * (-1/x)^3
= 10 * 4x^2 *-1/x^3
= 40x^2 * -1/x^3
= x ( 40 *-1/x)

4th term : 5C3 *(2x)^2 * (-1/x)^3
= 10 * 4x^2 *-1/x^3
= 40x^2 * -1/x^3
= x ( 40 *-1/x) <----- It is suppose to be only ( 40 *-1/x)

= 40x^2 * -1/x^3= 40*(-1)/x If you were asked to find the coefficient of -1/x then the answer would be 40 but they want the coefficient of 1/x
so we have -40*( 1/x ) Got it? I hope so

 

[sitooon]

doesn't matter whether you use log or ln.. you will get the same answer in the end as only the base is changed in one it's e and other 10... However it is preferred to use ln instead of lg because of presence of e(exponential) in some questions which can easily be resolved with ln.

Welcome back sayed
I tried to use both , i got the right answer with ln but a wrong answer with log!
you can even check it yourself , mj2010 , va'31 question 3

 

[Suchal Riaz]

Welcome back sayed
I tried to use both , i got the right answer with ln but a wrong answer with log!
you can even check it yourself , mj2010 , va'31 question 3

It's impossible. But when you use ln, when taking antilog use e^X instead of 10^x.

 

[ZaqZainab]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s04_qp_1.pdf

Question 9 ii and iii. With explanation please

For 9 ii
There is thing called dot product i hope you are familiar with it
For perpendicular ie 90 degrees the dot product is 0
AOC=90
So (OA).(OC)=0 <----- dot product
(1i+3j-1k).(4i+2j+pk)
= ((1*4)+(3*2)+(-1*p))=0
=(4+6-p)=0
p=10
For 9iii
first find the unit vector of AD ie OD-OA
AD=(-2i-3j+(q+1)k)
To find the length of AD find the modulus
ROOT OF((-2)^2 +(-3)^2 +(q+1)^2) = Length of AD here its 7
(4+9+(q+1)^2)=49
(q+1)^2 = 36 <--- expand using (a+)^2 = a^2 +2ab +b^2
q^2+2q+1=36
q^2+2q-35=0
q=5
q=-7

 

[Faaiz Haque]

Thanks

 

[sitooon]

Suchal Riaz
syed1995
Sorry for arguing , i had a very silly mistake !
I got the right ans with both!