• 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)

Statistics 1: Post Your Doubts Here

Messages
96
Reaction score
27
Points
28
Please someone help is required to solve this out :(

6 (i) A manufacturer of biscuits produces 3 times as many cream ones as chocolate ones. Biscuits are
chosen randomly and packed into boxes of 10. Find the probability that a box contains equal
numbers of cream biscuits and chocolate biscuits.


(ii) A random sample of 8 boxes is taken. Find the probability that exactly 1 of them contains equal
numbers of cream biscuits and chocolate biscuits.


(iii) A large box of randomly chosen biscuits contains 120 biscuits. Using a suitable approximation,
find the probability that it contains fewer than 35 chocolate biscuits.


This is from Nov 2002 P6 (S1)

Thanks.


3 times as many cream ones as chocolate ones therefore if chocolate is x then cream will be 3x so x+3x=1, 4x=1, x=1/4 and 3x =3/4
Using Binomial we get 10C5*(0.25)^5*(0.75)^5=0.0584

8C1*(0.0584)(1-0.0584)^7=0.307

mean=npq=120*0.25=30
variance=npq=120*0.25*0.75=22.5

P(X<35)~~~~ continuity correction we get P(X<34.5)
P(Z<(34.5-35)/sqr22.5))=P(Z<0.949)
=0.829
 
Messages
389
Reaction score
202
Points
53
3 times as many cream ones as chocolate ones therefore if chocolate is x then cream will be 3x so x+3x=1, 4x=1, x=1/4 and 3x =3/4
Using Binomial we get 10C5*(0.25)^5*(0.75)^5=0.0584

8C1*(0.0584)(1-0.0584)^7=0.307

mean=npq=120*0.25=30
variance=npq=120*0.25*0.75=22.5

P(X<35)~~~~ continuity correction we get P(X<34.5)
P(Z<(34.5-35)/sqr22.5))=P(Z<0.949)
=0.829
OMG ! Thanks a lot. You are great ! Thank you very much.
Btw are u giving for Oct/Nov 2012 exams?
 
Messages
389
Reaction score
202
Points
53
Me too on OCT/NOV 2012 !
Actually I'm giving for General Paper (8009)
Do you do Maths,Chemistry & Physics as well ?
 
Messages
330
Reaction score
191
Points
53
Amy Bloom :
Ending in 2: _ _ _ _ _ _ 2 = 6!
Ending in 6: _ _ _ _ _ _ 6 = 6!/2
Ending in 8: _ _ _ _ _ _ 8 = 6!/2

Ans = 6! + 6!/2 + 6!/2 =1440
 
Messages
109
Reaction score
41
Points
38
for question 7 (i)
"if each friend is standing next to his partner"
So If there are 7 couples,they can each stand as BG or GB,and there are 7 "BG or GB"
For the arrangement,it's 7! because any couple can stand first * 2! * 2! * 2!.....7 times because the couple can be BG or GB
which makes the final answer,7! * (2!)^7

for part ii
The Men can stand at 7! ways and the women can stand at 7! ways,and it can be all women and men or all men and women
so the answer is 7! * 7! * 2
Hope it helped :)
 
Messages
1,857
Reaction score
2,374
Points
273
Yup it did. Thanks ^_^
for question 7 (i)
"if each friend is standing next to his partner"
So If there are 7 couples,they can each stand as BG or GB,and there are 7 "BG or GB"
For the arrangement,it's 7! because any couple can stand first * 2! * 2! * 2!.....7 times because the couple can be BG or GB
which makes the final answer,7! * (2!)^7

for part ii
The Men can stand at 7! ways and the women can stand at 7! ways,and it can be all women and men or all men and women
so the answer is 7! * 7! * 2
Hope it helped :)
 
Messages
45
Reaction score
32
Points
18


let me try,
1st part...

the Z-value for 0.9 is 1.281,
P(X>5.2)=0.9
P(Z>-1.281)=0.9

therefore,.
-1.281= (5.2 - 2x) / x (x represent standard deviation since i don't know how to make the std deviation symbol appear.)
x = 7.23


2nd part...

Let m represent mean, s represent standard deviation

to know from (m-s) to (m+s), it took how many area,
we will search for this:
P( m-s < X < m+s)
= P ((m-s-m)/s < Z < (m+s-m)/s) )
= P (-1<Z<1)
= 0.8413-0.1587
= 0.6826

then 800 x 0.6826 = 546.08

so we will expect 546.08 observations are between that range.
 
Messages
70
Reaction score
13
Points
18
Q3-Probability Of scoring a 12:

You get odd number on the spinner: 3/5
You add the dices, you get 12 only from 6+6
So P(12)= 1/36

As they are succesive events p(12)= (3/5)*(1/36)
= 1/60

You get an even number on the spinner: 2/5
You multipy the dices- you get 12 in 4 ways
----2 *6, 6*2, 3*4, 4*3
P(12) = 4/36

As they are successive events as well: (2/5)*(4/36)
=2/45

To get the total probability of getting a 12, add the 2 above Ps as the two events abover are mutually exclusive:
2/45 + 1/60= 11/180

Now tp find out the conditional probablity
P(Even no.| get 12) = P(even no. Intersection 12) / P(12)

=(2/45)/(11/180)
=8/11


Q.5 I found this one easier

Suppose x= 320 + d

P(X<x)
P(Z< x-320/21.6)= 0.409

Let phi=¥

¥(x-320/21.6)= .409
(x-320/21.6)= ¥^-1(.409)

As .409 cant be read off the table, you will take negative value

X-320/21.6= -¥^-1(0.591)

Read off the table

X-320/21.6=- .230
X=324.968

X= 320+d
d= 4.968
~ 4.97
 
Top