Mock Paper Mark Scheme
Advanced Subsidiary/Advanced GCE
General Certificate of Education
Subject STATISTICS
Paper No. Mock S1
Question
number
1.
Scheme
Marks
Let J represent the weight of a Jar ∴ J ∼ N(260.00, 5.452)


∴ P( J < 266) = P  Z <
266 − 260 

5.45 
M1 A1
= P(Z < 1.10)
= 0.8643
A1
(NB: calculator gives 0.86453: accept 0.864 – 0.865)
Let C represent weight of coffee in a Jar ∴ C ∼ N(101.8, 0.722)


∴ P(C < 100) = P  Z <
100 − 101 .8 

0.72

M1 A1
= P(Z < −2.50)
A1
= 0.0062
∴ P(J < 266 & C < 100) = 0.8643 × 0.0062
= 0.0054
UA009018 – AS/Advanced GCE Mathematics: Mock Papers with Mark Schemes (Part 1)
M1
A1
(8)
Statistics S1 Mark Scheme
Question
number
2. (a)
(b)
Scheme
Marks
Mode = 23
B1 (1)
For Q 1 :
n
= 10.5 ⇒ 11th observation ∴ Q 1 = 17
4
For Q 2 :
n
23 + 24
1
= 21 ⇒ = 2 (21st & 22nd) observations ∴ Q 2 =
=
2
2
B1
23.5
B1
3n
For Q 3 :
= 31.5 ⇒ 32nd observation ∴ Q 3 = 31
4
(c)
10
20
30
40
M1 A1
50
Box plot
M1
Scale & label
M1
Q1, Q2, Q3
A1
11, 43
(4)
A1 (4)
Number of Daisies
(d)
(e)
From box plot or
Q2 – Q1 = 23.5 – 17 = 6.5
Q3 – Q2 = 31 – 23.5 = 7.5
(slight) positive skew
Back-to-back stem and leaf diagram
UA009018 – AS/Advanced GCE Mathematics: Mock Papers with Mark Schemes (Part 1)
B1
(1)
B1
(1)
(11)
Statistics S1 Mark Scheme
Question
number
3. (a)
Scheme
y=
− 467
200
B1
(can be implied)
∴ x = 2.5 y + 755 .0
M1
 − 467 
 + 755.0
 200 
= 2.5 
= 749.1625
Sy =
A1
(accept awrt 749)
9179  − 467 
−

200  200 
M1 A1
A1
∴ Sx = 2.5 × 6.35946
Standard deviation <
(b)
A1
2
= 6.35946
= 15.89865
Marks
(accept awrt 15.9)
2
(interquartile range)
3
Suggest using standard deviation since it shows less variation in the
lifetimes
UA009018 – AS/Advanced GCE Mathematics: Mock Papers with Mark Schemes (Part 1)
M1
A1
(9)
B1
B1
(2)
(11)
Statistics S1 Mark Scheme
Question
number
4. (a)
Scheme
Marks
P(correct at third attempt) = 0.4 × 0.4 × 0.6
M1
A1
= 0.096
(b)
a
P(A = a)
(c)
1
2
3
4
0.6
0.24
0.096
0.064
B1
All P(A = a) correct
B1
(accept awrt 0.974)
A1
E(A) = Σ a P(A = a) = (1 × 0.6) + . . . + (4 × 0.064)
M1
= 1.624
A1
(accept awrt 1.62)
E(A2) = Σ a2 P(A = a) = (12 × 0.6) + . . . + (42 × 0.064)
M1
= 3.448
A1
(2)
M1
∴ Var (A) = 3.448 – (1.624)2
= 0.810624
(2)
M1
P(correct number) = 1 – (0.4)4
= 0.9744
(d)
a = 1, 2, 3, 4
(2)
(accept awrt 0.811)
A1
(6)
F(1 + E(A)) = P(A ≤ 1 + E(A))
= P(A ≤ 2.624)
= 0.84
UA009018 – AS/Advanced GCE Mathematics: Mock Papers with Mark Schemes (Part 1)
M1
A1
(2)
(14)
Statistics S1 Mark Scheme
Question
number
Scheme
Marks
Sauna
5. (a)
0.35
Swim
Tree with correct
number of branches
M1
0.2, 0.3, 0.5
A1
All correct
A1
0.65
0.2
No Sauna
(3)
Sauna
0.2
0.3
Run
0.8
No Sauna
Sauna
0.5
0.45
Cycle
0.55
No Sauna
(b)
P(used sauna) = (0.2 × 0.35) + (0.3 × 0.2) + (0.5 × 0.45)
M1 A1
A1
= 0.355
(c)
P(swim | sauna used) =
=
P(swim & sauna)
P(sauna)
0.2 ×0.35
0.355
M1 A1
= 0.19718
(d)
P(swim | sauna not used) =
(accept awrt 0.197)
P(sauna
not used
P(sauna
swim)
P(swim)
not used)
P(sauna not used | swim) = 1 – 0.35 = 0.65
P(sauna not used)
= 0.20155
Scheme
UA009018 – AS/Advanced GCE Mathematics: Mock Papers with Mark Schemes (Part 1)
A1
(3)
M1
B1
= 1 – 0.355 = 0.645
M1 A1 f.t.
0.65 ×0.2
∴ P(swim | sauna not used) =
0.645
Question
(3)
M1
(accept awrt 0.202)
A1
(6)
(15)
Marks
Statistics S1 Mark Scheme
number
6. (a)
y
100
Scales & labels B1
Points B2, 1, 0 (3)


90

80
Temp
°C

70


60

50

15
25
35
45
55
x
Speed (mph)
(b)
(c)
Points lie reasonably close to a straight line
b=
a=
8 × 20615 − 260 × 589
11780
=
2
8 × 9500 − ( 260 )
8400
= 1.40238…
B1
(accept awrt 1.40)
589
 260 
 = 28.0476175… (accept awrt 28.0)
− (1.40238…) 
8
 8 
(1)
M1 A1
M1 A1 (4)
∴ y = 28.0 + 1.40 x
(d)
a ⇒ surrounding air temperature when tyre is stationary
B1
b ⇒ for every extra mph, temperature rises by 1.40 °C
B1
UA009018 – AS/Advanced GCE Mathematics: Mock Papers with Mark Schemes (Part 1)
(2)
Statistics S1 Mark Scheme
(e)
(f )
y = 28.0 + 1.40 × 50 = 98
B1
Regression line is only a line of best fit and does not necessarily pass
through all points
B1
12 mph – reasonable to use line; 12 is just below lowest x-value
B1; B1
85 mph – not reasonable to use line; 85 is well outside range of values
B1; B1 (4)
(2)
(16)
UA009018 – AS/Advanced GCE Mathematics: Mock Papers with Mark Schemes (Part 1)
Statistics S1 Mark Scheme
8
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