# Difficult Poisson distribution Question - S2 Edexcel

Watch
Announcements

Question:

The probability that a match will not strike is 0.009. Calculate the probability that in a box of 100 matches:

(a) they all strike satsfactorily

(b) at least 2 do not strike

The probability that a match will not strike is 0.009. Calculate the probability that in a box of 100 matches:

(a) they all strike satsfactorily

(b) at least 2 do not strike

0

reply

bump I tried everything but the calculator always gives me an error because 100! cannot be done.

0

reply

Report

#3

Shouldn't you be using Binomial? But the numbers are so big that you use Poisson as an approximation - therefore you use np and your lambda value for Poisson so multiply 0.009 by 100 and then use this number and use the possion equation.

0

reply

Report

#5

(Original post by

Can you guide me through this please, repped.

**The Joker**)Can you guide me through this please, repped.

ex- 100nCr100.

btw what are the answers?

0

reply

Report

#6

(Original post by

Shouldn't you be using Binomial? But the numbers are so big that you use Poisson as an approximation - therefore you use np and your lambda value for Poisson so multiply 0.009 by 100 and then use this number and use the possion equation.

**natty_d**)Shouldn't you be using Binomial? But the numbers are so big that you use Poisson as an approximation - therefore you use np and your lambda value for Poisson so multiply 0.009 by 100 and then use this number and use the possion equation.

or is that only a condition if you make it one? i'm not sure.

0

reply

The correct answers are:

(a) 0.4066

(b) 0.2275

How it got to there I don't know.

(a) 0.4066

(b) 0.2275

How it got to there I don't know.

0

reply

Report

#8

(Original post by

hmmm i don't think the poisson is the right distribution to use because the mean and the variance don't give about the same values?

or is that only a condition if you make it one? i'm not sure.

**zomgleh**)hmmm i don't think the poisson is the right distribution to use because the mean and the variance don't give about the same values?

or is that only a condition if you make it one? i'm not sure.

0

reply

Report

#9

(Original post by

The correct answers are:

(a) 0.4066

(b) 0.2275

How it got to there I don't know.

**The Joker**)The correct answers are:

(a) 0.4066

(b) 0.2275

How it got to there I don't know.

you can't use a normal coz p isn't close to 0.5.

can't use poisson coz mean and variance aren't about the same.

0

reply

Report

#10

(Original post by

i used the binomial formula for the 1st one- (0.991)^100 and got 0.4049, can't think of any other way.

you can't use a normal coz p isn't close to 0.5.

can't use poisson coz mean and variance aren't about the same.

**zomgleh**)i used the binomial formula for the 1st one- (0.991)^100 and got 0.4049, can't think of any other way.

you can't use a normal coz p isn't close to 0.5.

can't use poisson coz mean and variance aren't about the same.

0

reply

Report

#11

(Original post by

Yes, you're right - but if you work it out mean being np = 0.009 x 100 = 0.9 and variance = 0.9 (1-0.009)= 0.8919. They are so similar that you can use the Poisson distribution.

**natty_d**)Yes, you're right - but if you work it out mean being np = 0.009 x 100 = 0.9 and variance = 0.9 (1-0.009)= 0.8919. They are so similar that you can use the Poisson distribution.

but how would you divide by 100 factorial?

0

reply

**zomgleh**)

i used the binomial formula for the 1st one- (0.991)^100 and got 0.4049, can't think of any other way.

you can't use a normal coz p isn't close to 0.5.

can't use poisson coz mean and variance aren't about the same.

**: From previous experience of word-processing her work, a sociology student is known to make an average of**

Question

Question

**1.5**errors per complete page. The numbers of errors on different pages are independent.

(a) Find the probability that the essay will contain exactly

**10 errors.**

**P(X = 10)**so e-1.5 x 1.5^10 over 10!= 0.0000000035.

The correct answer is actually 0.0413.

0

reply

Report

#13

**The Joker**)

The correct answers are:

(a) 0.4066

(b) 0.2275

How it got to there I don't know.

Use Binomial, I think you must be calculating something wrong.

For question 2: you want at least 2 so the probability of they all strike satisfactorily + the probability of one not striking correctly taken away from 1.

So for P of 0 = from previous question you get 0.4049

then P of 1 = 100C1 x 0.009^1 x 0.991^ 99 = 0.3677

then 1 - (0.4049 + 0.3677) = 0.2774

I've obviously made a small rounding error but there you are.

0

reply

Report

#14

(Original post by

Okay thank you for your help, can you help me with this last question.

(a) Find the probability that the essay will contain exactly

The correct answer is actually 0.0413.

**The Joker**)Okay thank you for your help, can you help me with this last question.

**: From previous experience of word-processing her work, a sociology student is known to make an average of**

QuestionQuestion

**1.5**errors per complete page. The numbers of errors on different pages are independent.(a) Find the probability that the essay will contain exactly

**10 errors.****P(X = 10)**so e-1.5 x 1.5^10 over 10!= 0.0000000035.The correct answer is actually 0.0413.

0

reply

Report

#15

the S2 exam is in 9 days.

(Y)

And the sociology question should mention how many pages there are in the essay.

You then multiply the average rate (1.5) by that factor.

(Y)

And the sociology question should mention how many pages there are in the essay.

You then multiply the average rate (1.5) by that factor.

0

reply

(Original post by

Does it say that there's a certain amount of pages in her essay or something?

**natty_d**)Does it say that there's a certain amount of pages in her essay or something?

0

reply

Report

#17

can someone help me with the hypothesis testing using 2-tailed tests please?

thing is- I don't understand when you use p(x>/=) or p(x</=) ?

here's a link-

http://tinypic.com/view.php?pic=dpg7b7&s=6

why couldn't they have used-

p(x>/=) 35 instead??

thing is- I don't understand when you use p(x>/=) or p(x</=) ?

here's a link-

http://tinypic.com/view.php?pic=dpg7b7&s=6

why couldn't they have used-

p(x>/=) 35 instead??

0

reply

Report

#18

(Original post by

Sorry it has 4 pages my mistake.

**The Joker**)Sorry it has 4 pages my mistake.

0

reply

(Original post by

Then multiply 4 by 1.5 so you get the correct rate and then use the answer for your poisson distribution.

**natty_d**)Then multiply 4 by 1.5 so you get the correct rate and then use the answer for your poisson distribution.

0

reply

Report

#20

(Original post by

can someone help me with the hypothesis testing using 2-tailed tests please?

thing is- I don't understand when you use p(x>/=) or p(x</=) ?

here's a link-

http://tinypic.com/view.php?pic=dpg7b7&s=6

why couldn't they have used-

p(x>/=) 35 instead??

**zomgleh**)can someone help me with the hypothesis testing using 2-tailed tests please?

thing is- I don't understand when you use p(x>/=) or p(x</=) ?

here's a link-

http://tinypic.com/view.php?pic=dpg7b7&s=6

why couldn't they have used-

p(x>/=) 35 instead??

When you read the text it says that the 35 out of the hundred people were sold something.

35 < 45 (45% of 100) , so you go for that tail.

But yes, the question does seem a bit strange. I would have thought you should do both tails as H1 is P =/= 0.45. Is it from the S2 book?

0

reply

X

### Quick Reply

Back

to top

to top