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Original post by WaNaBe
June 2009 8. (c)

Context: A cloth manufacturer knows that faults occur randomly in the production process at a rate of 2 every 15 metres.

'A retailer buys a large amount of this cloth and sells it in pieces of length x metres. He chooses x so that the probability of no faults in a piece is 0.8.

Write down an equation for x and show that x = 1.7 to 2 significant figures.'

I'm not too sure how to tackle this question, I looked at the mark scheme but that hasn't exactly helped either. Any help would be appreciated.


Hi there, well I would tackle the problem like this: so we have a Poisson Distribution but we don't have lambda. So we have x metres of cloth, and a fault occurs twice every 15. So lambda will be 2x/15.

Now, we know now that the distribution is ~Po(2x/15), and P(X=0) = 0.8 (X being the number of errors). So all we have to do know is use the exponential form of the distribution, so we are left with e^(-2x/15) = 0.8

Now just solve this equation and we should be done! Hope this helps ^^
Original post by sweetascandy
Believe me, FUN is the last word I would use to describe FM! -__-
And no I'm going to UCL for economics :smile: Wbu?


You know what...stuff the invigilators - they can think whatever they want as long as I get my grade in the end :cool:
And nahh I think exams in Summer generally have lower grade boundaries because in January, it's mostly people that are like extra prepared who do it early; everyone else does it in June so I guess more variations potentially?


What word would you describe it with? :P

I'm going UCL too, to do physics.
Reply 102
Original post by Anonymous1994
Hi there, well I would tackle the problem like this: so we have a Poisson Distribution but we don't have lambda. So we have x metres of cloth, and a fault occurs twice every 15. So lambda will be 2x/15.

Now, we know now that the distribution is ~Po(2x/15), and P(X=0) = 0.8 (X being the number of errors). So all we have to do know is use the exponential form of the distribution, so we are left with e^(-2x/15) = 0.8

Now just solve this equation and we should be done! Hope this helps ^^


Thanks for the help, definitely made it much clearer. How do you know to make e^-2x/15 = 0.8 though? :smile:
Original post by Jukeboxing
What word would you describe it with? :P

I'm going UCL too, to do physics.


Disgusting! :p:
OMG, yaaayyy I've found another UCL buddy :smile: are you gunna live in halls or student house?
Original post by WaNaBe
June 2009 8. (c)

Context: A cloth manufacturer knows that faults occur randomly in the production process at a rate of 2 every 15 metres.

'A retailer buys a large amount of this cloth and sells it in pieces of length x metres. He chooses x so that the probability of no faults in a piece is 0.8.

Write down an equation for x and show that x = 1.7 to 2 significant figures.'

I'm not too sure how to tackle this question, I looked at the mark scheme but that hasn't exactly helped either. Any help would be appreciated.


i think this is right:

every x meters, you would expect 2x/15 faults

so y-po(2x/15)

using formula for poisson, p(x=0) is equal to e^-2x/15

this equation is equal to 0.8 as probabilty of 0 is 0.8

solve by taking ln and then then find out what x is
Original post by sweetascandy
Disgusting! :p:
OMG, yaaayyy I've found another UCL buddy :smile: are you gunna live in halls or student house?


I've applied for Halls.
Original post by Braniac101
Quick question to help everyone
WHAT IS THE GENERAL RULE FOR THE SF OR DECIMAL PLACES
I KNOW IF YOU USE TABLES YOU SAY SO AND DO 4 SF. BUT WHAT IF YOU DO THE QUESTION YOURSELF. WHAT IS MINIMUM AND HOW MANY SHOULD YOU DO?
i know m2 has 2/3 sf max


If you are doing binomial or poisson it should be four dp as its four on the tables.

Other than that it's anything sensible really. If possible, use fractions.
Original post by drewb
If you are doing binomial or poisson it should be four dp as its four on the tables.

Other than that it's anything sensible really. If possible, use fractions.


so have everones teachers reccomened 4 d.p on tables, and 3 otherwise?
Original post by WaNaBe
Thanks for the help, definitely made it much clearer. How do you know to make e^-2x/15 = 0.8 though? :smile:


The formula, (e^-lambda x lambda^X)/X!. You know that when X= 0, the probability is 0.8.

When you sub 0 into the formula, it simplifies down to e^-lambda = 0.8
Original post by Braniac101
so have everones teachers reccomened 4 d.p on tables, and 3 otherwise?


Mine does.
Great question if anyone wants to have a go:

S2C1EQ03.jpg

Spoiler

Original post by Dreamweaver
Great question if anyone wants to have a go:

S2C1EQ03.jpg

Spoiler



Great indeed :smile: Where is this from?
Could someone tell me how to do this? It's the fourth question from the June 2011 pastpaper.

"In a game, players select sticks at random from a box containing a large number of sticks
of different lengths. The length, in cm, of a randomly chosen stick has a continuous
uniform distribution over the interval [7, 10].

A stick is selected at random from the box.

(a) Find the probability that the stick is shorter than 9.5 cm.

To win a bag of sweets, a player must select 3 sticks and wins if the length of the longest
stick is more than 9.5 cm.

(b) Find the probability of winning a bag of sweets."

Part (a) is fine but how would you find part (b)?
Original post by sweetascandy
Believe me, FUN is the last word I would use to describe FM! -__-
And no I'm going to UCL for economics :smile: Wbu?


You know what...stuff the invigilators - they can think whatever they want as long as I get my grade in the end :cool:
And nahh I think exams in Summer generally have lower grade boundaries because in January, it's mostly people that are like extra prepared who do it early; everyone else does it in June so I guess more variations potentially?


True, true, screw the invigilators. And yeah, you're probably right for pretty much every module (about the grade boundaries being lower) but not M2 (or the FPs). There are pretty much no single maths people doing the M2 module (which is fair enough I guess, S2 or M1 are both sooo much easier) so it's FM student vs. FM student, all striving for the A*, so the grade boundaries won't change too much, might go down by like one mark - or even go up with FM students trying to up there UMS for an easier A* :redface: ah well, finger scrossed
First time I've seen this thread! But yeah S2 is pretty easy...
Original post by ezioaudi77
Could someone tell me how to do this? It's the fourth question from the June 2011 pastpaper.

"In a game, players select sticks at random from a box containing a large number of sticks
of different lengths. The length, in cm, of a randomly chosen stick has a continuous
uniform distribution over the interval [7, 10].

A stick is selected at random from the box.

(a) Find the probability that the stick is shorter than 9.5 cm.

To win a bag of sweets, a player must select 3 sticks and wins if the length of the longest
stick is more than 9.5 cm.

(b) Find the probability of winning a bag of sweets."

Part (a) is fine but how would you find part (b)?


Use the binomial distribution.

N is 3, P is the probability you worked out in (a). You're working out the P(x>9.5) so change that into something you can use the formula for then you have your answer!
Reply 116
Original post by Anonymous1994
The formula, (e^-lambda x lambda^X)/X!. You know that when X= 0, the probability is 0.8.

When you sub 0 into the formula, it simplifies down to e^-lambda = 0.8


Ohh yes, I see, thank you. :smile:
Reply 117
That june 2011 was hard ! :confused:
Does anyone know how to do question 7 part g and h? I've seen a few questions similar to part h but I just don't know how to do them! Help please? Much appreciated !
Original post by ezioaudi77
Great indeed :smile: Where is this from?


Its a question in the edexcel S2 book, i don't think in the papers they give so difficult questions.
Original post by raheem94
Its a question in the edexcel S2 book, i don't think in the papers they give so difficult questions.


I hope they don't :redface:

Btw, how would you attempt part b?

"In a game, players select sticks at random from a box containing a large number of sticks
of different lengths. The length, in cm, of a randomly chosen stick has a continuous
uniform distribution over the interval [7, 10].

A stick is selected at random from the box.

(a) Find the probability that the stick is shorter than 9.5 cm.

To win a bag of sweets, a player must select 3 sticks and wins if the length of the longest
stick is more than 9.5 cm.

(b) Find the probability of winning a bag of sweets."

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