• We need your support!

    We are currently struggling to cover the operational costs of Xtremepapers, as a result we might have to shut this website down. Please donate if we have helped you and help make a difference in other students' lives!
    Click here to Donate Now (View Announcement)

Mathematics: Post your doubts here!

Messages
785
Reaction score
2,290
Points
253
Guyz I need your preferance in terms of Calculators in Mathematics D version exams, I am appearing this time....
A, Which calculator you prefer (must contain all required features) ?
B, How much would it cost?
C, Where in Karachi I can buy it?


Thanks in advance...
 
Messages
116
Reaction score
66
Points
38
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.
 
Messages
144
Reaction score
107
Points
53

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)
 
Messages
20
Reaction score
19
Points
13
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)
 
Messages
20
Reaction score
19
Points
13
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
 
Messages
1,764
Reaction score
3,472
Points
273
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 :)
 
Messages
108
Reaction score
156
Points
53
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)
 
Messages
302
Reaction score
432
Points
28
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 ?
 
Messages
1,824
Reaction score
949
Points
123
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.
 
Messages
1,764
Reaction score
3,472
Points
273
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 :)
 
Messages
302
Reaction score
432
Points
28
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 :rolleyes:
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
 
Messages
1,764
Reaction score
3,472
Points
273
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
 
Top