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© The Independent Institute of Education (Pty) Ltd 2020
Page 1 of 11
MODULE NAME: MODULE CODE:
QUANTITATIVE TECHNIQUES B QUAT6211w
ASSESSMENT TYPE: ASSIGNMENT 1 (PAPER ONLY)
TOTAL MARK ALLOCATION: 100 MARKS
TOTAL HOURS: 10 HOURS
By submitting this assignment, you acknowledge that you have read and understood all the rules
as per the terms in the registration contract, in particular the assignment and assessment rules in
The IIE Assessment Strategy and Policy (IIE009), the intellectual integrity and plagiarism rules in
the Intellectual Integrity Policy (IIE023), as well as any rules and regulations published in the
student portal.
INSTRUCTIONS:
1. No material may be copied from original sources, even if referenced co
ectly, unless it is a
direct quote indicated with quotation marks. No more than 10% of the assignment may
consist of direct quotes.
2. Any assignment with a similarity index of more than 25% will be scrutinised for
plagiarism.
3. Make a copy of your assignment before handing it in.
4. Assignments must be typed unless otherwise specified.
5. All work must be adequately and co
ectly referenced.
6. Begin each section on a new page.
7. Follow all instructions on the assignment cover sheet.
8. This is an individual assignment – For group assignments, the group may not exceed 4
members and all will be awarded the same mark.
9. Round all final answers to two decimal places.
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© The Independent Institute of Education (Pty) Ltd 2020
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Referencing Ru
ic
Providing evidence based on valid and referenced academic sources is a fundamental educational
principle and the cornerstone of high quality academic work. Hence, The IIE considers it essential to
develop the referencing skills of our students in our commitment to achieve high academic
standards.
Poor quality formatting in your referencing will result in a penalty of a maximum of five (5) marks
against the percentage mark awarded, according to the following guidelines. Please note, however,
that evidence of plagiarism in the form of copied or uncited work (not referenced), absent
eference lists, or exceptionally poor referencing, may result in action being taken in accordance
with The IIE’s Intellectual Integrity Policy (0023).
Required Subtract 1 Subtract 2 Subtract 3 Subtract 4 Subtract 5
• Cons istent in-
text
eferencing
s tyle
• Quotation
marks , page
numbers,
years , etc.
applied
co
ectly
• Only one or
two minor
mistakes in
s tyle made
• Al l sources
are
accurately
eflected and
included in a
eference l ist
• Cons istent in-
text referencing
s tyle
• Quotation
marks , page
numbers, years,
etc. applied
co
ectly
• Fewer than five
minor mistakes
made
• More than 90%
of the sources
are co
ectly
eflected and
included in a
eference l ist
• Cons istent in-
text
eferencing
s tyle
• Quotation
marks , page
numbers,
years , etc. not
a lways
applied
co
ectly
• Not a l l
paraphrased
content
eferenced
• At least 80%
of the sources
are co
ectly
eflected and
included in a
eference l ist
• Cons istent
in-text
eferencing
s tyle
• Quotation
marks used
for di rect
quotes but
page
numbers
missing
• At least 70%
of the
sources are
co
ectly
eflected
and
included in
a reference
l i st
• In-text
eferencing
used but
inconsistent
• Paraphrased
material cited
ut not
eferenced
accurately or
cons istently
in text
• Quotation
marks and/or
page numbers
for di rect
quotes
missing
• At least 60%
of the sources
are co
ectly
eflected and
included in
eference l ist
• Poor and
inconsistent
eferencing
s tyle used
• At least 50%
of the
sources are
co
ectly
eflected
and included
in reference
l i st
• Quotation
marks
and/or page
numbers for
di rect quotes
missing
• May be
efe
ed for
action in
accordance
with IIE 0023
Intellectual
Integrity
Policy
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© The Independent Institute of Education (Pty) Ltd 2020
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Learning Area: Ve
al Communication
The primary objective of numeracy concepts in the business environment is to provide essential
tools to deal with the increasing amounts of information you are bombarded with, not only in the
usiness environment but also in your everyday life through newspapers, magazines, television,
adio and the internet.
Numeracy concepts in the business environment include some mathematical calculations and
statistical methods. A sound knowledge of mathematics and statistics is the cornerstone for
various quantitative activities and good decision-making in economics, business, industry,
education, defence, science, medicine and engineering.
Task:
As a Quantitative Techniques student, you are required, to complete this statistical assignment by
applying your knowledge from Learning Units 1—4, consulting various sources such as books and
internet sources.
NOTE: You are required to do this assignment individually. Bear in mind that you may do rese arch
outside the content of the textbook.
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© The Independent Institute of Education (Pty) Ltd 2020
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Question 1 XXXXXXXXXXMarks: 25)
Give all final answers as percentages to two decimal places.
Q.1.1 The following contingency table gives the results of a sample survey of South
African male and female respondents with regard to their prefe
ed cellphone
service provider:
Q.1.1.1 What is the probability of randomly selecting a male respondent from
the sample?
(1)
Q.1.1.2 What is the probability of randomly selecting a respondent who is
female and prefers MTN?
(2)
Q.1.1.3 What is the probability of selecting a male respondent, given that the
prefe
ed provider is Cell C?
(2)
Q.1.1.4 What is the probability of selecting a respondent who is male or who
prefers Vodacom?
(3)
Q.1.1.5 What is the probability of selecting a respondent who does not prefer
Vodacom?
(2)
Q.1.2 Events X and Y are such that ?(?) = 0.45 and ?(? ∪ ?) = 0.85. Given that X
and Y are independent and non-mutually exclusive, determine ?(?).
(5)
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Q.1.3 A bag contains 14 red and six blue ma
les. You are asked to select two ma
les
from the bag. The first ma
le selected will not be placed back into the bag.
Q.1.3.1 Construct a probability tree for the various possible outcomes that
may occur.
(7)
Q.1.3.2 What is the probability that the two ma
les selected will be different
colours?
Note: Give your final answer as a percentage to two decimal places.
(3)
Question 2 XXXXXXXXXXMarks: 25)
Give all final probability answers as percentages to two decimal places.
Q.2.1 It has been found that 1 out of every 10 visitors to a museum buys something
from the gift shop. If we randomly select a sample of 12 visitors to the
museum, what is the probability that no more than three of the visitors will
uy something from the gift shop? Interpret your answer.
(5)
Q.2.2 It has been found from experience that an exclusive clothes shop makes an
average of four sales every fifteen minutes. If we randomly select a fifteen
minute period, what is the probability that the shop will make:
Q.2.2.1 More than one sale? Interpret your answer. (5)
Q.2.2.2 Less than three sales? Interpret your answer. (5)
Q.2.3 It has been found that the time taken to complete an emotional intelligence
test is normally distributed, with an average time (μ) of 18 minutes and a
standard deviation (σ) of 3.5 minutes. What is the probability that a randomly
selected person will take:
Q.2.3.1 Between 15 and 17 minutes to complete the test? Interpret your
answer.
(5)
Q.2.3.2 More than 20 minutes to complete the test? Interpret your
answer.
(5)
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Question XXXXXXXXXXMarks: 25)
Give your final answers as percentages to two decimal places.
Q.3.1 The weight of grapefruits produced by an orchard is normally distributed, with a
mean weight (μ) of 450g and a standard deviation of 50g. We randomly select a
sample of 120 grapefruits from the orchard.
Q.3.1.1 Compute the standard e
or. (2)
Q.3.1.2 What is the probability that the average weight of the grapefruits in the
sample will lie between 445g and 460g? Interpret your answer.
(7)
Q.3.2 Experience has shown that 15% of municipal rates bills contain an estimated
amount for electricity usage. We randomly select a sample of 75 rates bills.
Q.3.2.1 Compute the standard