Answer key

1 (a) Weight gain (b) , , n = 150

(i) Mean = 3.2867 kg (ii) Standard deviation = 2.3291 kg

(c) 2.8 or 2.9 (d) 0.627 or 0.498

2 (a) 0.18 (b) 0.5 (c) 0.2

3 (a) 0.0424 (b) 0.9740

4 (a) (i) refer graph (ii)negative correlation, points scatter about a line with negative gradient

(b) 0.1524 The two scores have a weak positive correlation.

5 (a) 52.94; 51.63 (b) The Laspeyres price index uses base year quantities as the weights but the Paasche price index uses current year

quantities as the weights.

6 Q Y centred m.a., T Y - T seasonal index Y - S

1 2.8

-0.8962

3.696

2 4.2

0.4688

3.731

3 3.0 3.68

-0.68 -0.5412

3.541

4 4.6 3.70

0.90 0.9688

3.631

5 3.0 3.76

-0.76 -0.8962

3.896

6 4.2 3.88

0.32 0.4688

3.731

7 3.5 3.93

-0.43 -0.5412

4.041

8 5.0 3.99

1.01 0.9688

4.031

9 3.0 4.06

-1.06 -0.8962

3.896

10 4.7 4.11

0.59 0.4688

4.231

11 3.6

-0.5412

4.141

12 5.3

0.9688

4.331

Q1 Q2 Q3 Q4

2011

-0.68 0.9

2012 -0.76 0.32 -0.43 1.01

2013 -1.06 0.59

-0.91 0.455 -0.555 0.955

-0.0138 -0.0138 -0.0138 -0.0138

-0.8962 0.4688 -0.5412 0.9688

7 (a) Refer graph (b) Points lie about a straight line (c) A = 29.02, b = 3.90 (d) Evaporation loss increases 3.90 ml for each additional week (e) (i) 103.12 ml, still acceptable because evaporation loss after 19 weeks is very closed to the data collected

(ii) 165.52 ml, unreliable because evaporation loss after 35 weeks is way outside the range of the data collected.

8 (a) Area is more than 1 for function g. Probability density function cannot be negative.

(b) (i)

(ii) (iii) median = 12

P(12 < x < 12.16) = 0.0337