910370
1SUPERVISOR’S USE ONLY
9 1 0 3 7
© New Zealand Qualifications Authority, 2017. All rights reserved.No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.
ASSESSOR’S USE ONLY
TOTAL
Level 1 Mathematics and Statistics, 201791037 Demonstrate understanding of chance and data
9.30 a.m. Monday 20 November 2017 Credits: Four
Achievement Achievement with Merit Achievement with ExcellenceDemonstrate understanding of chance and data.
Demonstrate understanding of chance and data, justifying statements and findings.
Demonstrate understanding of chance and data, showing statistical insight.
Check that the National Student Number (NSN) on your admission slip is the same as the number at the top of this page.
You should attempt ALL the questions in this booklet.
Show ALL working.
If you need more space for any answer, use the page(s) provided at the back of this booklet and clearly number the question.
Check that this booklet has pages 2 – 16 in the correct order and that none of these pages is blank.
YOU MUST HAND THIS BOOKLET TO THE SUPERVISOR AT THE END OF THE EXAMINATION.
TRANSPORTATION
http://www.trademe.co.nz/motors/news-reviews/20161005-local-corolla-offers-extra-value/
QUESTION ONE
(a) Ngaire wants to buy a car. She took a sample of cars and drew a graph of the age of the cars (in years) and the distance they had travelled (in kilometres).
0
0
10 000
20 000
30 000
40 000
50 000
60 000
70 000
80 000
90 000
100 000
2 4 6 8 10 12Age (years)
Distance travelled vs car age
Dis
tanc
e tra
velle
d (k
m)
State the relationship that exists between the age of cars and the distance they have travelled AND find the average change in distance travelled by a car each year as the age increases.
Justify your answer.
2
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
(b) Ngaire produced another graph which compared a car’s original price ($) with its percentage decrease in value per year (depreciation).
5 000 10 000 15 000 20 000 25 000 30 000
0
10
20
30
40
50
60
Original price ($)
Percentage decrease in value vs original price
Perc
enta
ge d
ecre
ase
in v
alue
(per
yea
r)
(i) Describe any features visible in the graph of the original price and percentage decrease in value per year.
3
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
(ii) In terms of percentage decrease in value, is it better to buy a cheaper or more expensive car?
Justify your answer.
4
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
(c) In 2016, the Ministry of Transport released a report.
It looked at a sample of 298 drivers charged by police with reckless driving, and displayed it as shown below:
15–1920–24
25–2930–34
35–3940–44
45–4950–54
55–5960–64
65–6970–74
75–7980+
0
5
10
15
20
25
30
35
40
Driver age group (years)
Female
Male
Vehicle drivers charged with reckless driving
Num
ber o
f driv
ers c
harg
ed w
ith re
ckle
ss d
rivin
g
32
5
35
12
8
19
13
5
15
8
17
6
14
7 7
13
4
13
6 7
2
6
24 5
12
15
6
(i) What was the probability that a randomly selected driver from the sample of drivers charged with reckless driving in 2016, was a male aged 20–24?
(ii) What was the probability that a randomly selected driver from the sample of female drivers charged with reckless driving in 2016, was in the 15–24 age group?
(iii) Based on the 2016 sample, how many times more likely was it that, chosen at random, a vehicle driver who was charged with reckless driving, would be a male than a female?
5
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
QUESTION TWO
(a) The popularity of colours for different types of vehicles is shown below. The numbers shown are a percentage.
BlackBlueGreenLight brownOthersRedSilverWhite / White pearlYellow / GoldYellow / OrangeGrey
0% 20% 40% 60% 80% 100%
13 10 4 6 11 16 26 1 13
15 6213 2 15 18 10 4 15
22 7 23 7 16 25 6 12
10 13 4 10 10 25 12 4 12
SUV / Truck / Van
Type of vehicle
Sport / Compact
Luxury
Full / Intermediate / Sedan
(i) What is the most popular colour in luxury vehicles?
Justify your answer.
(ii) What other ways could you display this data?
State the advantages and disadvantages of each method.
6
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
7
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
(b) The display below compares the carbon dioxide emissions (in g / km) of a sample of 100 cars made in 1984 compared to the carbon dioxide emissions of a sample of cars made in 2016.
0 100 200 300 400 500 600 700
CO2 g / km
1984
2016
Carbon dioxide emissions and year builtmin: 135.47lq: 226.80med: 264.49mean: 279.46uq: 308.58max: 694.30sd: 90.43num: 100
min: 0lq: 197.81med: 255mean: 247.65uq: 283.75max: 410sd: 58.57num: 100
(i) What is the difference between the median amounts of carbon dioxide emissions in g / km of cars built in 1984 and those built in 2016?
(ii) Which year of build has the greatest variation in carbon dioxide emissions?
Justify your answer.
8
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
(iii) Comment on the distribution of carbon dioxide emissions for both 1984-built and 2016-built cars.
Note any similarities and differences as well as any unusual features.
(iv) Car manufacturers claim that ‘cars produced in 2016 tend to produce less carbon dioxide than cars made in 1984.’
Use statistical reasoning, based on this sample of cars, to comment on the car manufacturers’ claim.
Justify your answer clearly.
9
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
QUESTION THREE
(a) The New Zealand police record the details of all vehicles stolen.
The top 15 vehicle models stolen in a 6-month period in 2015 are shown below.
Ford CourierFord Falcon
Holden CommodoreHonda Accord
Mazda 323 / FamiliaMitsubishi Lancer
Nissan PrimeraNissan Safari
Nissan SkylineNissan Terrano
Subaru ImprezaSubaru LegacyToyota Corolla
Toyota HiaceToyota Hilux
0 20 40 60 80 100 120 140 160Number of vehicles stolen
Vehi
cle
mak
e an
d m
odel
Top 15 stolen vehicle models in a 6-month period in 2015
(i) How many Nissan Primeras were stolen in this 6-month period?
(ii) “Nissan was the most stolen make of vehicle in the 6-month period in 2015.” State whether you think this sentence is true, giving statistical reasons for your answer.
10
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
(iii) AA Insurance released its top 10 stolen vehicle models from 1 May 2013 to 30 April 2014:
1. Honda Torneo 2. Subaru Impreza 3. Mazda Premacy 4. Mazda Familia 5. Subaru Forester 6. Mazda Atenza 7. Subaru Legacy 8. Mazda MPV 9. Nissan Sunny 10. Nissan Cefiro
This list is quite different from the police data.
Give statistical reasons for these differences.
11
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
(b) The New Zealand Transport Agency (NZTA) counts the number of vehicles using major roads. It then compares the results from the same period in the previous year. The information below shows the travel growth of All Vehicles and the travel growth of Heavy Vehicles only.
–8%Jan 2008 Jan 2009 Jan 2010 Jan 2011 Jan 2012 Jan 2013 Jan 2014 Jan 2015 Jan 2016
–6%
–4%
–2%
0%
2%
4%
6%
8%
All vehicles Heavy vehiclesMonth and year
Trav
el g
row
th
Travel growth of vehicles on New Zealand roads
(i) In what year did travel growth reach its lowest point for Heavy Vehicles?
Justify your answer.
12
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
(ii) Based on the results shown, what could possibly happen to the travel growth in 2017 and 2018 for All Vehicles?
State at least two possibilities, giving statistical reasons for your answers.
(iii) When analysing the results, the NZTA takes the mean of the previous 3 months’ data and plots that result on the graph (e.g. the January 2016 result that is plotted comes from the mean of the November 2015, December 2015, and January 2016 results).
Give statistical reasons why you think the NZTA does this.
13
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
14
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
QUESTION NUMBER
Extra paper if required.Write the question number(s) if applicable.
15
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
QUESTION NUMBER
Extra paper if required.Write the question number(s) if applicable.
91
03
716
Mathematics and Statistics 91037, 2017
ASSESSOR’S USE ONLY
QUESTION NUMBER
Extra paper if required.Write the question number(s) if applicable.