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19; 20 2020 © 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 correctly, 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 correctly 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. 19; 20 2020 © The Independent Institute of Education (Pty) Ltd 2020 Page 2 of 11 Referencing Rubric 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 reference 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 referencing s tyle • Quotation marks , page numbers, years , etc. applied correctly • Only one or two minor mistakes in s tyle made • Al l sources are accurately reflected and included in a reference l ist • Cons istent in- text referencing s tyle • Quotation marks , page numbers, years, etc. applied correctly • Fewer than five minor mistakes made • More than 90% of the sources are correctly reflected and included in a reference l ist • Cons istent in- text referencing s tyle • Quotation marks , page numbers, years , etc. not a lways applied correctly • Not a l l paraphrased content referenced • At least 80% of the sources are correctly reflected and included in a reference l ist • Cons istent in-text referencing s tyle • Quotation marks used for di rect quotes but page numbers missing • At least 70% of the sources are correctly reflected and included in a reference l i st • In-text referencing used but inconsistent • Paraphrased material cited but not referenced accurately or cons istently in text • Quotation marks and/or page numbers for di rect quotes missing • At least 60% of the sources are correctly reflected and included in reference l ist • Poor and inconsistent referencing s tyle used • At least 50% of the sources are correctly reflected and included in reference l i st • Quotation marks and/or page numbers for di rect quotes missing • May be referred for action in accordance with IIE 0023 Intellectual Integrity Policy 19; 20 2020 © The Independent Institute of Education (Pty) Ltd 2020 Page 3 of 11 Learning Area: Verbal 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 business environment but also in your everyday life through newspapers, magazines, television, radio 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. 19; 20 2020 © The Independent Institute of Education (Pty) Ltd 2020 Page 4 of 11 Question 1 (Marks: 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 preferred 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 preferred 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) 19; 20 2020 © The Independent Institute of Education (Pty) Ltd 2020 Page 5 of 11 Q.1.3 A bag contains 14 red and six blue marbles. You are asked to select two marbles from the bag. The first marble 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 marbles selected will be different colours? Note: Give your final answer as a percentage to two decimal places. (3) Question 2 (Marks: 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 buy 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) 19; 20 2020 © The Independent Institute of Education (Pty) Ltd 2020 Page 6 of 11 Question 3 (Marks: 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 error. (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