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Dibm 0126: Business Mathematics 2 Question Paper
Dibm 0126: Business Mathematics 2
Course:Diploma In Procurement & Logistics Management
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF
DIPLOMA IN BUSINESS MANAGEMENT &
DIPLOMA IN PROCUREMENT & LOGISTICS MANAGEMENT
DIBM 0126: BUSINESS MATHEMATICS 2
STREAMS: DIBM & DPLM Y1S2 TIME: 2 HOURS
DAY/DATE: WEDNESDAY14/8/2013 8.30 A.M. – 10.30 A.M.
INSTRUCTIONS:
Answer question One and any other two questions.
All working must be shown clearly
Adhere to the instructions in your answer booklet
Do not write anything on the question paper.
QUESTION ONE: (30 MARKS)
Briefly define the following terms giving examples in each case as used in set theory.
Universal set
Sub-set
Compliment of a set
Union of two sets
Set enumeration [10 marks]
The human resource department of a company has records which show the following analysis of its 200 engineers.
Age
Years Diploma Certificate
only Bachelors degree
only Total
<30 90 10 100
30-40 20 30 50
>40 40 10 50
Total 150 50 200
Required:
Find the probability that an engineer selected at random
Has only a bachelors degree [2 marks]
Has a diploma certificate only [2 marks]
Has a bachelors degree given that he is over 40 years [2 marks]
He is under 30 years given that he has only a diploma certificate [2 marks]
A committee of 4 must be chosen from 3 women and 4 men.
Calculate how many ways the committee can be chosen. [3 marks]
A local used car dealer gets complaints about his car as shown below:
No. of complaints x 0 1 2 3 4 5 6
Frequency f
1 5 15 26 33 14 6
Probability
Find the expected number of complaints. [3 marks]
Find the determinant cofactors and hence the inverse of the following matrix:
[¦(-2&7&2@6&-6&0@4&10&3)] [6 marks]
QUESTION TWO: (20 MARKS)
Use the inverse method to solve for the unknown in the following system of linear equations.
?3x?_1+?4x?_2+?3x?_3=60
? 4x?_1+?10x?_2+?2x?_3=104
? 4x?_1+?2x?_2+?4x?_3=60 [15 marks]
For a fixed length of time, the probability of a worker error on a certain production line is 0.1 the probability that an accident will occur when there is a worker error is 0.3 & the probability that an accident will occur when there is no worker error is 0.2. Find the probability of a worker error if there is an accident. [5 marks]
QUESTION THREE: (20 MARKS)
Suppose that an insurance company has broken down the yearly automobile claims for the drivers aged 16 – 21 as shown
Amount of claim probability
(x) (Pi)
0 0.7
2000 0.10
4000 0.05
6000 0.03
8000 0.01
Required:
How much should the company charge as its average premium in order to breakeven on its cost for claims. [5 marks]
Give brief definition of the following terms:
The decision maker
Courses of action
States of nature
Pay-off
Uncertainty [10 marks]
Two projects have been considered and it is required that we determine the preferred project. Use the information below to make the decision. (Use expectation).
Project A Ksh Prob
Optimistic outcome 6000 0.2
Most likely outcome 3500 0.5
Pessimistic outcome 2500_ 0.3
12000 1.0
Project B Ksh Prob
Optimistic outcome 6500 0.1
Most likely outcome 4000 0.6
Pessimistic outcome 2000_ 0.3
12000 1.0
[5 marks]
QUESTION FOUR: (20 MARKS)
If Ksh 1000 is deposited for 6 years in an account paying 8% per year compounded semi annually
Find (i) The compound amount
(ii) The actual amount of interest [6 marks]
For how many years must Sh.1000 be invested at 10% per annum in order to accumulate to Sh.1610.50. [5 marks]
An annuity will pay 8000 at the end of each year for 5 successive years. The 1st payment being 12 months from the initial purchase date, what is the maximum price any rational investor would pay for such annuity if the opportunity cost for capital is 10%?
[5marks]
An investment opportunity involves an initial capital of 50000 and it gives an annual return of 5000 starting in 12 months’ time and continuing indefinitely. The capital can be invested elsewhere at 8% interest.is this a worthy investment? [4 marks]
QUESTION FIVE: (20 MARKS)
An investor has to choose between 2 projects A and B whose initial capital & returns are presented in the table below. Which one is a better investment if the current rate of interest 8%?
Project A Project B
Value of initial capital 30,000 30,000
Return in 1st year 6,000 8,000
2nd year 10,000 8,000
3rd year 10,000 8,000
4th year 10,000 8,000
5th year 8,000 8,000
[10 marks]
The table below summarises the opinion of various groups on the issue of gay marriages. What is the probability that a person selected at random of these groups of people is
a non-white
a non-white and favours gay marriages
favours gay marriages given that the person is non-white [10 marks]
White Non-white
Opinion Rep Demo Rep Demo Total
Favours 300 100 25 10 435
Oppose 100 250 25 190 565
total 400 350 50 200 1000
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