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ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD (Department of Business Administration) ***** BUSINESS MATHEMATICS & STATISTICS (8532) CHECKLIST SEMESTER: AUTUMN 2016 This packet comprises the following material: 1. 2. 3. 4. Text Book (two) Supplementary material (one) Assignment No 1 & 2 Assignment Forms (2 sets) If you find anything missing out of the above-mentioned material, please contact at the address given below: Mailing Officer Mailing Section, Block-28 Allama Iqbal Open University H-8, ISLAMABAD. Phone: 051-9057611-12 Prof. Dr. Syed Hassan Raza Course Coordinator ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD (Department of Business Administration) WARNING 1. 2. PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE. SUBMITTING ASSIGNMENT(S) BORROWED OR STOLEN FROM OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN “AIOU PLAGIARISM POLICY”. Course: Business Mathematics & Statistics (8532) Level: (MBA (2½ Years)/M.Com) Semester: Autumn 2016 Total Marks: 100 Pass Marks: 50 ASSIGNMENT No. 1 Q. 1 (a) A data processing manager purchased remote terminal processing time to run special jobs at two different computer “utilities”. She wishes to sign a long-term contract with the firm whose computer causes the least delay on the average. The numbers of minutes of delayed processing per week were obtained during trial periods with each firm and are provided below: Compu Quick 210 15 47 93 104 Dail-a-Pute 18 314 523 25 19 293 115 203 Assuming that trial experience is representative of future performance, which firm should receive the business? Substantiate your answer with appropriate calculations. (b) The length of life 220 incandescent 60-watt lamps was obtained and yielded the frequency distribution shown in the table given below: Class Limit Frequency 550-559 3 600-699 7 700-799 14 800-899 28 900-999 64 1000-1099 57 1100-1199 23 1200-1299 13 1300-1399 7 1400-1499 4 1. Construct a histogram of these data, using a vertical scale for relative frequencies. 2. Find the mean length of life 3. Find the standard deviation (10+10)= 20 2 Q. 2 An electronic fuse is produced by five production lines in a manufacturing operation. The fuses are costly quite reliable and shipped to suppliers in 100- unit lots. Because testing is destructive, most buyers of the fuses test only a small number of fuses before deciding to accept or reject lots of incoming fuses. All five production lines produce fuses at the same rate and normally produce only 2% defective fuses, which are randomly dispersed in the output. Unfortunately, production line I suffered mechanical difficulty and produced 5% defective during the month of March. This situation became known to the manufacturer after the fuses had been shipped. A customer receive a lot produced in March and tested three fuses. One failed. What is the probability that the lot was produced on line-I? What is the probability that the lot came from one of the four other lines? (20) Q. 3 a. b. A foreman in a manufacturing plant has three men and three women working for him. He wants to choose two workers for a special job. Not wishing to show any biases in his selection, he decided to select the two workers at random. Let Y denote the number of women in his selection. Find the probability distribution for Y. (20) The achievement scores for a college entrance examination are normally distributed with a mean of 75 and a standard deviation of 10. What fraction of the scores would you expect to lie between 70 and 90? Q. 4 The shopping times were recorded for 64 randomly selected customers for a local supermarket. The average and variance of the 64 shopping times were 33 minutes and 256, respectively. Estimate the true average shopping time per customer, µ, with a confidence coefficient of I- = 0.90 (20) Q.5 A vice-president for a large corporation claims that salesmen are averaging no more than 15 sales contacts per week. (She would like to increase this figure) As check on her claim, 36 salesmen are selected at random, and the number of contacts is recorded for a single randomly selected week. The sample reveals a mean of 17 contacts and a variance of 9. Does the evidence contradict the vice-president’s claim? Use = 0.50. (20) ASSIGNMENT No. 2 Total Marks: 100 This assignment is a research-oriented activity. Write a paper of about 10 pages on the topic allotted to you. Prepare two copies of this report; submit one copy to your tutor for evaluation and the other for presentation in the class, which will be held at the end of semester prior to your final examination. You may use transparencies, charts or any other material for effective presentation. You are required to select one of the following topics according to the last digit of your roll number. For example, if your roll number is D-3427185 then you will select topic number 5 (the last digit). (1) The Binomial Distribution (2) The Normal Distribution 3 (3) (4) (5) (6) (7) (8) (9) (10) Measures of Dispersion Measures of Variation System of Equations Measures of Relationship. Sampling Methods and Techniques in Business Statistics Time Series Analysis in Forecasting Test of Hypothesis Differentiation and their Application in Business BUSINESS MATHEMATICS AND STATISTICS COURSE OUTLINE (M.Com-8532) BLOCK–1 DESCRIPTIVE STATISTICS Introduction to Statistics Role of Statistics in Business Constructing a Frequency Distribution Graphing Frequency Distribution Measures of Central Tendency Choosing Measures of Central Tendency Percentiles, Deciles and Quartiles Measures of Dispersion Range and Semi-Interquartile Range Variance, Standard Deviation Coefficient of Variation Chebyshev’s Inequality BLOCK-2 PROBABILITY Sample Spaces and Events Definitions of Probability Addition and Multiplication Rules of Probability Conditional Probability Baye’s Theorem Probability Distribution Discrete Probability Distribution Expected Values and Variance Continuous Probability Distribution The Binomial Distribution The Poisson Distribution Hypergeometric Distribution The Normal Distribution BLOCK–3 SAMPLING AND SAMPLING DISTRIBUTION Population and Sample Parameters and Estimators 4 Reasons for Sampling Random Sampling Stratifies Random Sampling Systematic Sampling Cluster Sampling Sampling Distributions Point and Interval Estimation Determination of Sample Size BLOCK–4 TESTING OF HYPOTHESIS The rationale of Hypothesis Testing Type of Errors Testing Hypothesis about One Mean Testing Hypothesis about Two Means Testing Hypothesis about Proportions Goodness of Fit Contingency Table Analysis BLOCK–5 REGRESSION AND CORRELATION ANALYSIS The Functional Relationship between Two Variables Scatter Diagram Linear Correlation Inferences Concerning Correlation Coefficient The Linear Regression Equation The Principle of Least Squares Estimating Regression Equation Coefficient of Determination Multiple Regression and Correlation Analysis BLOCK–6 TIME SEREIS AND INDEX NUMBERS Introduction to Time Series Components of Time Series Measures of Trend and Seasonal Variation Time Series Analysis in Forecasting Defining and Index Number Unweighted Aggregate Index Price, Quantity and Value Indices CPI and its Uses BLOCK–7 SET THEORY AND SYSTEM OF LINEAR EQUATIONS Set Theory, Types of sets Methods of Representing sets Venn Diagram Solution of Linear Systems System of Linear Equations and its Applications Linear Inequalities 5 Quadratic Inequalities BLOCK–8 MATRICES Introduction to Matrix Addition and Multiplication of Matrices Row Operations Determinant Inverse of a Matrix Systems of m Equations in n Unknowns Applications of Matrices in Business BLOCK–9 DIFFERENTIATION AND INTEGRATION The Instantaneous Rate of Change Rules of Differentiation Relative Maxima and Relative Minima Test for Determination of Maxima and Minima The Indefinite Integral The Definite Integral Methods of Integration Application in Business TEXT BOOKS: 1. Levin, D. and Rubin, D., “Statistics of Management”7th Ed. PrenticeHall Int. 2. Mason, R.D and Lind, D.A., “Statistical Techniques in Business and Economics”, 9th Ed. 3. Wheeler / Peoples “Modern Mathematics” 4th Ed. Published by Brooks? Cole Publishing 4. Budnick,. F.S “Applied Mathematics for Business, Economics and the Social Sciences” McGraw Hill Ltd. ____[]____ 6