Final Version
January 2005 6683 Statistic S1 Mark Scheme
Question Number
Scheme
Marks
1 (a) Faulty 0.03
Goodbuy 0.85
0.97 Not faulty Faulty
0.15
0.06 Amart 0.94
Tree (both sections) M1 labels & 0.85,0.15 or equiv. A1 Not faulty 0.03,0.97,0.06,0.94 A1 (3)
(b)
valid path & their values, correct P(Not faulty) =(0.85 0.97)+(0.15 0.94) % or 1931/2000 or equiv. or awrt 0.966 0.9655
M1,A1∫ A1 (3) (Total 6 marks)
6683 Statistics S1 January 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics
Question Number
2 (a)
Scheme
Q1 33, Q2 41, Q3 52
Marks
B1B1B1 (3)
(b)
(6)
(c)
Median of Northcliffe is greater than median of Seaview. Upper quartiles are the same IQR of Northcliffe is less than IQR of Seaview Northcliffe positive skew, Seaview negative skew Northcliffe symmetrical, Seaview positive skew (quartiles) Range of Seaview greater than range of Northcliffe any 3 acceptable comments B1B1B1 (3)
(d)
On 75% of the nights that month both had no more than 52 caravans on site.
B1 B1 (2) (Total 14 marks)
6683 Statistics S1 January 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics
Question Number
Scheme
Marks
3(a)
S1 Jan 2005 Question 3(a) 90
80
182, 80 184, 77
172, 77 165, 72
Weight (y)
70
175, 70
162, 65 60
164, 59 156, 56 152, 52 155, 49
50 147, 44 40
148, 39
30 140
150
160
170
180
190
Height (x)
sensible scales B1 labels B1 shape B1 (3)
6683 Statistics S1 January 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics
Question Number
Scheme
(b)
Positive; as x increases, y increases
(c)
1962 740 S xy 122783 1793 12
Marks
context OK
B1;B1g (2)
use of formula, cao
M1A1
(1793 only M1A1) (2)
(d)
b
S xy S xx
1793 1.027507... 1745
division, 1.028
M1A1
(SR 1.028 B1 only) (2)
(e) y
740 2 61 12 3
61
2 or 61.6 or 61.7 B1 3
2
47746 740 s 13.26859... 12 12
Use of formula including root, 13.3 or 13.9 M1A1
(SR 13.3 or 13.9 B1 only) (3)
(f)
34-36, 87-89
strict limits,3sf or better B1B1 (2)
(g)
All values between their 35.7 and their 87.7 so could be normal. Reason required B1
6683 Statistics S1 January 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics
(1) (Total 15 marks)
Question Number
4 (a)
Scheme
k 2k 3k 4k 5k 1 15k 1 1 ** k ** 15
Marks
verification / use of
P(X x) 1
M1
cso A1 (2)
(b)
P(X 4) P(1)+P(2)+P(3)
1 2 3 + + 15 15 15 2 = 5
=
sum of 3 probabilities M1 0.4 or
6 2 or A1 seen (2) 15 5 (2)
(c)
(d)
1 2 3 4 5 E(X ) 1 2 3 4 5 15 15 15 15 15 11 3
use of
xP(X x) M1
55 11 2 or or 3 or 3.6 or 3.67 A1 15 3 3
E(3X 4) 3E(X ) 4 11 4 7
(2) 3xtheirs-4 M1 A1 seen (2)
(OR
E(3X 4) 1 7
1 2 3 4 5 2 5 8 11 15 15 15 15 15
(3x 4)kx cao
M1 A1) (2) (Total 8 marks)
6683 Statistics S1 January 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics
Question Number
Scheme
Marks
5 (a) A
B
6 subtract 4,5,7 subtract 16,19,25 box & 918
16 19
5
6
B1 M1 A1 M1 A1 B1 (6)
4 7
25 C
918
918 0.918 1000
(b)
P(No defects)=
(c)
918+16+19+25 56 47 OR 1 P(No more than 1)= 1000 1000
B1∫ (1) M1 0.978 A1∫
=0.978
(2)
(d)
P( B Only 1 defect)
19 P(B and 1 defect) 1000 = 16 19 25 P(1 defect) 1000 19 60
conditional prob M1
19 or 0.316 or 0.317 A1∫ 60 (2)
(e) P(Both had type B)=
37 36 theirs from B x M1 1000 999 37 cao A1 or 0.0013 or 0.00133 or equivalent 27750 (2) (Total 13 marks)
6683 Statistics S1 January 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics
Question Number
Scheme
Marks
6(a)
(Discrete) Uniform
B1
(b)
e.g.Tossing a fair dice / coin
B1g
(c)
Useful in theory – allows problems to be modelled not necessarily true in practice
B1g B1h
(d)
Carry out an experiment to establish probabilities
B1g B1h
(1) (1)
(2)
(2) (Total 6 marks)
6683 Statistics S1 January 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics
Question Number
7 (a)
(b)
Scheme
P(X 70)
70 79 ) 12 P(Z 0.75) 0.2266
P(Z
standardise 79, 12 or 79, 144 M1 + or -0.75, 0.2266
64-79 96 79 P(64<X 96) P( Z ) 12 12 + or -1.25&1.42, 0.8166
Marks
A1A1 (3)
standardise both, 79& 12 only M1 Accept 0.8160-0.8170
A1,A1 (3)
(c) Shaded area =
1 (1 0.6463) 3
=0.1179
M1A1 cso
A1 (3)
(d)
P(X 79 b) 0.7642 b 0.72 12 b 8.64
0.7642 standardise LHS = z-value, all correct 3sf
B1 implied M1A1 A1 (4) (Total 13 marks)
6683 Statistics S1 January 2005 Advanced Subsidiary/Advanced Level in GCE Mathematics