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AQA S1B 17th May 2013 AM - Unofficial Markscheme

UNOFFICIAL MARKSCHEME

Question 1 - Mean, Standard Deviation and Linear Scaling - 7 Marks

1ai) Mean = 62.3{F}
Standard Deviation = 16.8{F} (2; A1 62.3CAO, A1 16.8CAO) -- Note; answers >1dp will be rejected

b) Mean = 16.8{C}
Standard Deviation = 9.33{C} (3; B1 5/9(mean ai - 32), A1 16.8, A1 9.33)

c) r = 0.997 - Linear Scaling does not affect PMCC (2; A1 0.997, E1 Valid Explanation)

Question 2 - Normal Distribution - 13 Marks

2ai) P(X=421) is 0 (1; A1 CAO) -- Ignore any working

2aii) P(X<425) is 0.945 (2; M1 Use of formula, A1 0.945 CAO -- condone >3sf)

2aiii) P(418<X<424) is 0.770 (3; M1 Use of formula, M1 P(<424)-P(<418) etc, A1 0.770)

2b) (3)

2c) P(Y<410)... Mean = 417 (4)

Question 3 - Binomial Distribution - 11 Marks

3ai) P(X<=10) is 0.970 (1; A1 0.970 CAO)

3aii) P(X>=25) is 0.077 (2; M1 1-p(<=24), A1 0.077)

3aiii) P(X=2) is 0.0160 (2; M1 use of formula nCr x p^r x (1-p)^n-r, A1 0.0160)

3aiv) P(10<X<15) is 0.451 (4)

3b) E(x) = 27 (2; M1 Use of formula E(x), A1 27 CAO)

Question 4 - Regression - 17 Marks

4ai) PMCC between g and y = 0.911

4aii) PMCC between l and y = 0.640 (Total 3 for ai and aii)

4b) Showing that both have strong positive correlations (or other positive qualifiers) and therefore stating, as girth increases, weight increases, and as length increases, weight increases (3)

4ci) PMCC between x and y = 0.984
Therefore x and y has strongest correlation (2; A1 0.984, E1 x AND y have the strongest correlation)

4cii) X (Estimated Weight) = 124.5{kg} (2; M1 Subbing of values, A1 124.5kg)

4ciii) y = 0.46 + 1.00(1)x (3; Answers of 0.6 for 'a' will be penalised)

4civ) Showing that estimate is relatively accurate using y=0.46+1x to get 125.1... Also stating 124.5 is likely accurate due to PMCC of 0.984 (4)

Question 5 - Probability - 11 Marks

5ai) P = 0.855

5aii) P = 0.14 (Total 3 for ai and aii)

5bi) P = 0.72 (2)

5bii) P = 0.684 (2)

5biii) P = 0 (1; A1 CAO)

5biv) P = 0.0425 (3)

Question 6 - Confidence Intervals and Normal Distribution - 16 Marks

6ai) Mean = 19.9
So CI = 19.9 +/- 0.186 (Accept 19.7-20.1) (5; A1 Mean = 19.9, M1 use of formula, M1 use of z(0.99) = 2.3263, M1 Correct Substitution of all values, A1 Correct Answer)

6aii) 20 enclosed in 98% CI, so likely to be true, but possibly not... (Any valid explanation) (2)

6aiii) Approximately Normally Distributed already (1; E1 Any valid explanation - REJECT references to sample size)

6bi) Mean <25 - probability is 0.012 (4; Use of sd/rt(n), finding z, getting the answer )

6bii) > 25 in the 10 bags - probability is 0.065 (4; Normal Distribution for p>25... then to the power 10)

Thanks to Son234 for some of the answers

Total: 75
M1 = Marking Point
A1 = Answer
E1 = Explanation
- I have done this roughly, it may not be right... it is just for you to gauge how you did...

(edited 10 years ago)

Scroll to see replies

Reply 1

Sayonara

6bii) > 25 in the 10 bags - probability is 0.065 (4; Normal Distribution for p>25... then to the power 10)

Oops, I did 0.98809^10. :L

Reply 2

PrinceUpsb

4ci I seem to remember a value of 0.982 opposed to your 0.984. Are you certain?

Reply 3

PrinceUpsb

Also where does this 'Note; answers >1dp will be rejected' come from?

Reply 4

steviep14

Original post by PrinceUpsb

4ci I seem to remember a value of 0.982 opposed to your 0.984. Are you certain?

Maybe... but I think that is pretty insignificant... haha
if I can be bothered, I'll re-do the question at some point :smile:

Reply 5

steviep14

Original post by PrinceUpsb

Also where does this 'Note; answers >1dp will be rejected' come from?

The fact the question clearly stated "to 1 decimal place"... will mean, an answer given to a different accuracy will not be accepted I'd assume

Reply 6

Sayonara

Original post by steviep14

The fact the question clearly stated "to 1 decimal place"... will mean, an answer given to a different accuracy will not be accepted I'd assume

OMDZ, it actually did... I am so unlucky today.

Reply 7

Chatirito_MUFC

I think answer to regression line is: y = 0.6 + x
Because: y - y(bar) = Sxy/Sxx (x - x(bar))
Therefore: y - 116.0 = 1.00 (x - 115.4)
Which is: y - 116.0 = 1.00x - 115.4
Which is: y = 1.00x + 0.6

Therefore: y = 0.6 + 1.00x

Shouldn't that be it?

Reply 8

PrinceUpsb

Original post by steviep14

Maybe... but I think that is pretty insignificant... haha
if I can be bothered, I'll re-do the question at some point :smile:

Haha no I agree, just thought perhaps I'd worked it out wrong in the exam!

Original post by steviep14

The fact the question clearly stated "to 1 decimal place"... will mean, an answer given to a different accuracy will not be accepted I'd assume

Ah didn't spot this but am very fortunate in that I remember doing this anyway.

Reply 9

steviep14

Original post by Chatirito_MUFC

no... why have you used 1.00x...
b was not 1.00... it was 1.001....
do not round numbers early... it is costly

Reply 10

Chatirito_MUFC

Original post by steviep14

no... why have you used 1.00x...
b was not 1.00... it was 1.001....
do not round numbers early... it is costly

Aah I see what you're saying.

Reply 11

kingmango

Predicted grade boundaries anyone?

Yes! Thank you

For standard deviation on Q1 I got 17.5 from my calculator. I used 'sx', is this wrong?

Reply 14

Jp1234

I got 0.00425 for 5biv. Did you by any chance forgot to enter another 0? :mad:

Reply 15

Segadfx

Original post by bg***j2

For standard deviation on Q1 I got 17.5 from my calculator. I used 'sx', is this wrong?

No, that would not be wrong. From past mark schemes, they will usually offer a range of answers for the mean and standard deviation, so it shouldn't matter whether you used sx.

Reply 16

wasia

Original post by AlanDu

Oops, I did 0.98809^10. :L

Did you get an answer of 0.887? Because i did x>25 (normal distribution tables) and i got that as well...

Reply 17

wasia

Original post by steviep14

UNOFFICIAL MARKSCHEME
6bii) > 25 in the 10 bags - probability is 0.065 (4; Normal Distribution for p>25... then to the power 10)

Can you remember what the standard deviation for that question was?

Reply 18

bleap

For the very last question, why was the answer not (1- the previous answer)^10 and also, how many marks would you expect me to lose for doing this method rather than the correct one as stated in the mark scheme?