Business Mathematics and Statistics MBA 523

ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD
(Department of Business Administration)
BUSINESS MATHEMATICS & STATISTICS (MBA-523)
CHECKLIST
SEMESTER: AUTUMN 2012
This packet comprises the following material:
1. Text Book (two)
2. Supplementary material on Business Mathematics
3. Course Outline
4. Assignment No 1 & 2
5. 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
Tanvir Ahmed
Course Coordinator
 ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Business Administration)
WARNING
1. 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.
2. SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN “AIOU PLAGIARISM POLICY”.
ASSIGNMENT No. 1
Course:  Business Mathematics & Statistics (523)    Semester: Autumn 2012
Level:  MBA (2½ Years)  /  MBA (3 ½ Years) Total Marks: 100
Pass Marks: 50
Note: All questions carry equal marks.

Q. 1 (a) Given the following data sets:
Class       10-19     20-29 30-39    40-49 50-59
Class Frequency       15        12     8        5     2
1. Represent the data with the help of histogram
2. Calculate mean and median
3. Calculate standard deviation (10)    

(b) The Vice President of sales for the conglomerate you work for has asked you to evaluate the sales records of two of the firm’s divisions.  You note that the range of monthly sales for division A over the last 2 years is Rs.50,000 and the range of division B is only Rs.30,000. You compute each division’s mean monthly sales for the same time period and discover that both divisions have a mean of Rs. 110,000. Assume that is all the information you have about the division’s sales records.  Would you be willing to say which of the divisions has a more consistent sales record? Why or why not? (10)

Q. 2 (a) Assume that the length of time, x, between charges of a pocket calculator is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. Find the probability that the calculator will last between 30 and 70 hours between charges. (10)

(b) A machine that produces stampings for automobile engines is malfunctioning and producing 10% defectives. The defective and non-defective stampings proceed from the machine in a random manner. If the next five stampings are tested, find the probability that three of them are defective. (10)

Q. 3 A soft drink machine is being regulated so that the amount of drink dispensed averages 240 milliliters with standard deviation of 15 milliliters. Periodically, the machine is checked by taking a sample of 40 drinks and computing the average content. If the mean of 40 drinks is a value within the interval x + 2 x, the machine is thought to be operating satisfactorily, otherwise adjustment is made. The company officials found that the mean of 40 drinks be 236 milliliters and concluded that the machine needed no adjustment. Was this a reasonable decision? Justify your answer. (20)

Q. 4 A company purchases large quantities of naphtha in 50-gallon drums. Because the purchases are ongoing, small shortages in the drums can represent a sizeable loss to the company. The weights of the drums vary slightly from drum to drum, so the weight of the naphtha is measured after removing it from the drums. Suppose the company samples the contents of 20 drums, measures the naphtha in each, and calculates mean 49.7 gallons and standard deviation 0.32 gallons. Do the sample statistics provide sufficient evidence to indicate that the mean fill per 50-gallon drum is less than 50 gallons? Use  = 0.10. (20)

Q. 5 (a) A research physician conducted an experiment to investigate the effects of various cold-water temperatures on the pulse rate of small children. The data for seven 6-year-old children are:
Child: 1 2 3 4 5 6 7
Temperature of water (oF): 68 65 70 62 60 55 58
Decrease in pulse rate: 2 5 1 10 9 13 10
(beats per minute)
1. Find the least squares line for the data
2. Plot the data and the fitted line (10)

(b) Explain the difference between regression and correlation problems. Can a correlation problem also be a regression problem? (10)

ASSIGNMENT No. 2
(Total Marks: 100)

This assignment is a research-oriented activity. 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). Visit any business/commercial organization and write a paper of about 1000 words on the topic allotted to you. Prepare two copies of this report; submit one copy to your tutor for evaluation and use other for presentation in the workshop, which will be held at the end of semester prior to your final examination.
(1) Probability and their Application in Business
(2)      Prediction and Regression
(3)      System of Equations
(4)      Measures of Relationship
(5)      Sampling Methods and Techniques in Business Statistics
(6)      Time Series Analysis  
(7)      Estimation and Hypothesis Testing
(8)      Analysis of Variance
(9)      Differentiation and their Application in Business.
(10)    Integration

BUSINESS MATHEMATICS AND STATISTICS
COURSE OUTLINE (MBA-523)
Course:  Business Mathematics & Statistics Course Code: 523
Level:  MBA Credit Hours: 03

UNIT–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

UNIT –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

UNIT –3 SAMPLING AND SAMPLING DISTRIBUTION
 Population and Sample
 Parameters and Estimators
 Reasons for Sampling
 Random Sampling
 Stratifies Random Sampling
 Systematic Sampling
 Cluster Sampling
 Sampling Distributions
 Point and Interval Estimation
 Determination of Sample Size

UNIT–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

UNIT–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

UNIT–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

UNIT–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
 Quadratic Inequalities

UNIT–8 METRICES
 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

UNIT–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

Recommended Books:
1. Richard I. Levin and David S. Rubin, Statistics for management 7th Ed. USA: Prentice Hall International Inc.
2. Mason, R.D and Lind, D.A Statistical Techniques in Business and Economics, 10th Ed. Richard D. Irwin.
3. Wheeler/Peeples, Modern mathematics 4th Ed. USA: Brooks/Code Pub Co.
4. Budnick, F. S. Applied Mathematics for Business, Eco. And the Social Sc. 4th Ed. McGraw-Hill Inc.