# Imm Gsm Stats Paper - Mathematics Essay Example

Page 1 of 3 ASSIGNMENT 2ND SEMESTER : STATISTICAL ANALYSIS (STAT) STUDY UNITS COVERED DUE DATE TOTAL MARKS : CHAPTERS 1 – 8 : 3. 00 p. m. 17 AUGUST 2010 : 100 INSTRUCTIONS TO CANDIDATES FOR COMPLETING AND SUBMITTING ASSIGNMENTS The complete ‘Instructions to Students for Completing and Submitting Assignments’ must be collected from any IMM GSM office, the relevant Student Support Centre or can be downloaded from the IMM GSM website. It is essential that the complete instructions be studied prior to commencing your assignment. The following points highlight only a few important notes. 1) You are required to submit ONE assignment per subject. ) The assignment will contribute 20% towards the final examination mark, and the other 80% will be made up from the examination, however the examination papers will count out of 100%. 3) Although your assignment will contribute towards your final examination mark, you do not have to earn credits for admission to the examinations; you are automatically accepted on registering for the exam. 4) Number all the pages of your assignment (e. g. page 1 of 4) and write your name and surname, student number and subject at the top of each page. 5) The IMM GSM requires assignments to be presented on plain A4 paper.

You must show all working calculations, including and where appropriate multiple choice working calculations. 6) A separate assignment cover, which is provided by the IMM GSM, must be attached to the front cover of each assignment. 7) Retain a copy of each assignment before submitting, in case the original does not reach the IMM GSM. 8) The assignment due date refers to the day up to which assignments will be accepted for marking purposes. The deadline is 3:00 p. m. on the 17 August 2010. Late assignments will be accepted, but 25 marks will be deducted from the maximum mark, if received after 3:00 p. m. on the 17 August 2010 and up to 5:00 p. . the following day, after which no assignments will be accepted. 9) If you fail to follow these instructions carefully, the IMM Graduate School of Marketing cannot accept responsibility for the return of the assignment. It may even result in your assignment not being marked. Results will be available on the IMM GSM website, www. immgsm. ac. za, on Friday, 8 October 2010. Assignment 2nd Semester 2010 © IMM Graduate School of Marketing Statistical Analysis (STAT) Page 2 of 3 SPECIFIC INSTRUCTIONS: • • • • • • Answer ALL the questions. Read each question carefully to determine exactly what is required before attempting the question.

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Where applicable, formulae and computations must be shown, failing which, marks will not be awarded. Answers must be set out in a systematic way under appropriate headings and sub-headings. Number your answers clearly. Graph paper is not required but graphs must be neat and according to scale. QUESTION 1 [10] The following data represents the percentages of monthly family income allocated to clothing for a sample of 50 shoppers: Percentages 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 1. 1 Frequency 6 14 16 10 4 Construct a relative frequency distribution for this set of data. Show all calculations correct to 2 decimal places.

Calculate the class boundaries and the class midpoints and include them in the relative frequency distribution. (8) Interpret the relative frequency of the class 10 – 19. (2) [10] 1. 2 QUESTION 2 2. 1 With reference to Question 1. 1, calculate the values of the arithmetic mean ( x ) and the variance ( S 2 ). (6) With reference to Question 1. 1, construct a histogram from the relative frequency distribution. Graph paper is not required, but the graph must be neat and according to scale. (4) 2. 2 Assignment 2nd Semester 2010 © IMM Graduate School of Marketing Statistical Analysis (STAT) Page 3 of 3

QUESTION 3 [10] A consumer testing service obtained the following fuel consumption figures, in litres per 100 kilometres, in five test runs performed with each of the three trucks. Truck A Truck B Truck C 3. 1 27,9 31,2 28,6 30,4 28,7 29,1 30,6 31,3 28,5 31,4 28,5 32,1 31,7 31,3 29,7 Measure the variation of the consumption figures of Truck A using the range. (1) Calculate the value of the third quartile of the consumption figures of Truck C. Interpret your answer. (4) If the manufacturers of Truck B want to advertise that their truck performed best in this test, which one of the ‘averages’, i. e. ean, median or mode, would be the most accurate to substantiate their claim? Give a reason for your answer. Show all calculations. (5) [10] 3. 2 3. 3 QUESTION 4 The manager of a restaurant claims that only 5% of the customers are dissatisfied with the service. Assume that this claim is true. 4. 1 What is the probability that the number of dissatisfied customers in a random sample of 20 customers will be at least one? (5) What is the probability that the number of satisfied customers in a random sample of 20 customers will be between 16 and 18, inclusive. Show all calculations correct to 4 decimal places. 5) [10] 4. 2 QUESTION 5 The number of customers who make use of the helpline facility at a firm is distributed as a Poisson random variable with a mean of two customers per hour. 5. 1 5. 2 What is the probability that more than three customers will make use of this helpline during a particular hour? (5) What is the probability that fewer than four customers will make use of this helpline during a four hour period? Show all calculations correct to 4 decimal places. (5) ASSIGNMENT TOTAL: 50 x 2 = 100 Assignment 2nd Semester 2010 © IMM Graduate School of Marketing Statistical Analysis (STAT)