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SUPERVISOR'S USE ONLY
NEW ZEALAND QUALIFICATIONS AUTHORITY
MANA TOHU MATAURANGA 0 AOTEAROA
Level 1 Mathematics and Statistics, 2013
91037 Demonstrate understanding of chance and data
9.30am Wednesday 13 November 2013
Credits: Fou r
Achievement
Demonstrate understanding of chance
and data.
Achievement with Merit
Demonstrate understanding of chance
and data, justifying statements and
findings.
Achievement with Excellence
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 2-11 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.
Low
Excellence
TOTAL
19
ASSESSOR'S USE ONLY
© New Zealand Qualifications Authority, 2013. All rights reserved.
No part of this publication may be reproduced by any means without the prior permission of the New Zealand Qualifications Authority.
3
2
You are advised to spend 60 minutes answering the questions in this booklet.
QUESTION ONE
Metua has been researching the amount of data being transmitted by local businesses near his home.
The graph for the amount of data transmitted each hour over 4 days is given below.
Business Data Volumes
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D ay and Time
(a)
Describe any overall trends that the graph shows_over the space of these 4 days.
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Mathematics and Statistics 91037, 2013
Mathematics and Statistics 91037, 2013
5
4
(b)
QUESTION TWO
Nikita is not confident that the claim in this advertisement is true.
ASSESSOR'S
USE ONLY
Give at least tw. atistical reasons hy Nikita might not trust the claims until she found out
more about the . tiug"'-~
Nikita saw the following advertisement in a sports magazine.
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The company claims that Herbolt helps sprinters to lower their sprint times.
The company tested 20 sprinters and recorded each sprinter'sfirst sprint time to run 100m.
Each sprinter then drank some Herbolt Energy Drink.
Finally, after 2 hours, each sprinter ran a second 100 m sprint, and the time was recorded.
The advertisement included the following graph, and claimed that this showed how well the product
worked to help sprinters to lower their sprint times.
100m Sprint Times
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Before Herbolt
(first sprint)
(a)
After Herbal!
(second sprint)
How much difference did the Herbolt Energy Drink make to the times, according to this
graph?
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Mathematics and Statistics 91037,2013
7
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(d)
Nikita did some research on the internet and found more results from the testing. The data is
summ~rised in the table below.
issessoil•s
From this data, do you think that it is true that Herbolt Energy Drink helps sprinters to lower
·-use·oNLY ·
their time to run 100 m?
Give reasons for your conclusion.
·yes
100m average times (seconds)
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Second Sprint
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first sprint (20 splinters)
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13.9
Sprinters NOTdrinking Herbolt Energy
Drink (15 sprinters)
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(c)
Draw a graph to clearly and accurately compare how the 100 m average times changed from
the first test to the second test.
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Use the grid below, and be sure to label your graph clearly.
If you
need to
redraw
this
graph,
use the
grid on
page 10.
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This research has used average times for I 00 m races . Th: research
use the median or the mean as their average.
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b. wonder if they should l'5' [L.'""'~[
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What would you recommend?
Give statistical reasons for your answer.
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QUESTION THREE
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Marino is helping to organise a gala at his school. He is going to use the two spinners drawn below:
(b)
From Marino's results, what is the probability that a player will spin a total of more than 10?
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If Marino spins the Spinner A; what is the probability that the ·arrow points to 2 or 6?
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Will Marino in ake a profit after 100 games?
Use theoretical probability to support your answer.
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If the total from the 2 spinners is more than 10, the player will win $10.
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The player will spin each spinner once only.
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Mar ino plans to offer a game where the player can win $10.
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If you need to redraw your answer to Question Two (c), draw it on the graph below. Make sure it is
clear which graph you want marked.
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