Download - Allama Iqbal Open University

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