[uxa595]

7

The volume of bleach in a 5-litre bottle may be modelled by a random variable with a standard deviation of 75 millilitres.
The volume, in litres, of bleach in each of a random sample of 36 such bottles was measured. The 36 measurements resulted in a total volume of 181.80 litres and exactly 8 bottles contained less than 5 litres.
(a) Construct a 98% confidence interval for the mean volume of bleach in a 5-litre bottle. (5 marks)
(b) It is claimed that the mean volume of bleach in a 5-litre bottle exceeds 5 litres and also that fewer than 10 per cent of such bottles contain less than 5 litres.
Comment, with numerical justification, on each of these two claims. (3 marks)
(c) State, with justification, whether you made use of the Central Limit Theorem in constructing the confidence interval in part (a).



7a
5.05 ± 0.3
7b
CI of 98% is above 5L, plus the mean (181.8/36) is above 5L THEREFORE, true claim
8/36 (22.2%) of the bottles are below 5L THEREFORE, untrue claim

What is 7c though ?




One other question :
Jumbo packets are also filled from the bin. Each filled jumbo packet contains
exactly 100 paper clips.

It is claimed that the proportion of red paper clips in the bin is greater than 0.22 and that jumbo packets do not contain random samples of paper clips.

An analysis of the number of red paper clips in each of a random sample of 50 filled jumbo packets resulted in a mean of 22.1 and a standard deviation of 4.17 .

Comment, with numerical justification, on each of the two claims. (3 marks)



Mean is 22.1/100 which is above 0.22 as a probability which would mean the claim is true. HOWEVER, the standard deviation is large (18%) of the mean value, and so the claim is not true.

What is the bold bit though ?
Is it just that 50 samples are used and that is a large number hence the claim is untrue as it does contain a random sample.

[claret_n_blue]

Regarding the first part, 7c, do you know what the Central Limit Theorem is?

[uxa595]

(Original post by claret_n_blue)
Regarding the first part, 7c, do you know what the Central Limit Theorem is?

Yup.
But i don't know how you would word it.

[claret_n_blue]

(Original post by uxa595)
Yup.
But i don't know how you would word it.

Ok first, what is it (just so I know you understand it)?

Secondly, how did you calculate the confidence interval?

[uxa595]

(Original post by claret_n_blue)
Ok first, what is it (just so I know you understand it)?

Secondly, how did you calculate the confidence interval?

The distribution of the sample mean is seen as normal given the sample is large enough.
I self taught myself it so but as far as i can tell the golden number here is 30 for aqa as a bog enough sample size.

X+- z(o/sq(n))
Where x is mean
N is sample size
O is SD


This was posted from The Student Room's iPhone/iPad App

[uxa595]

Also what about the other Q
Was i right?


This was posted from The Student Room's iPhone/iPad App

[claret_n_blue]

(Original post by uxa595)
The distribution of the sample mean is seen as normal given the sample is large enough.
I self taught myself it so but as far as i can tell the golden number here is 30 for aqa as a bog enough sample size.

X+- z(o/sq(n))
Where x is mean
N is sample size
O is SD

Ok yes, the Central limit theorem bit is correct. You've missed out explaining one more thing in the CI formula. The 'z' bit. What does that stand for? Can you see a link between that and what your theorem?

Just to let you know, I don't know if your answer to your CI is correct, I haven't checked that, I'm just helping you understand the last part.

[uxa595]

(Original post by claret_n_blue)
Ok yes, the Central limit theorem bit is correct. You've missed out explaining one more thing in the CI formula. The 'z' bit. What does that stand for? Can you see a link between that and what your theorem?

Just to let you know, I don't know if your answer to your CI is correct, I haven't checked that, I'm just helping you understand the last part.

It is correct. It was my exam i did this is and it's what everyone else got :P

I don't know much about the z value. I just take it out the formula book.


I've done the exam, i just wanted to know what those 2 answers are


Also, any idea about the other question?

[claret_n_blue]

(Original post by uxa595)
It is correct. It was my exam i did this is and it's what everyone else got :P

I don't know much about the z value. I just take it out the formula book.


I've done the exam, i just wanted to know what those 2 answers are


Also, any idea about the other question?

Not sure about the second question.

Yeah, you take it out the formula book, but where in the formula book?

MASSIVE HINT:

Spoiler:

Show

Which tables are you using?