Subject: QUANTITATIVE TECHNIQUES IN BUSINESS (QTB)

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  • 15 Marks

PSAF – May 2018 – L2 – Q5 – The Budgeting Process in the Public Sector

Explains the concept of a national budget, surplus and deficit budget implications, and challenges in the implementation of national budgets in Nigeria.

In government’s quest to optimally develop and efficiently manage available resources, national budgets are usually prepared to put economic development firmly on course.

Required:

a. Describe briefly a national budget. (3 Marks)

b. Explain briefly the implication of each of the following for the performance of the economy: i. A surplus budget ii. A deficit budget (4 Marks)

c. Explain FOUR problems to be encountered in the effective implementation of national budgets in Nigeria. (8 Marks)

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  • 20 Marks

QTB – Nov 2014 – L1 – SB – Q6 – Mathematics of Business Finance

Calculate the value of an investment with compound interest, the payoff amount for a loan with simple interest, and the additional interest for a loan with monthly payments and reduced interest rates.

a. If N250,000 is invested in an account that earns 4% per year compound interest, what is the:
i. value of the investment after 5 years? (3 Marks)
ii. total interest earned? (2 Marks)

b. When it was apparent that your parents could not afford to finance your university education, you sought and obtained a 4-year loan of N250,000.00 from Education Bank Limited. The bank imposed a simple interest rate of 7½%.
i. How much do you need to pay off the bank now

(4 years after) that you are through with your study?

(7 Marks)
ii. If you decide to be paying N25,000 every month from now and the bank agreed to reduce the interest rate to 1% per month on the unpaid balance at the beginning of the month, how much additional total interest will be paid? (8 Marks)

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  • 10 Marks

QTB – Nov 2014 – L1 – SB – Q5b – Data Collection Analysis

Draw a frequency polygon and an ogive based on gasoline mileage data from an experiment.

In a particular organisation, an experiment which was conducted to determine the gasoline mileage of a particular type of car yielded the following data:

Miles per gallon Percent
10 and under 12 4
13 and under 15 8
16 and under 18 14
19 and under 21 26
22 and under 24 12
25 and under 27 11
28 and under 30 10
31 and under 33 7
34 and under 36 6
37 and under 39 2

Required:

i. Draw the frequency polygon for gasoline mileage. (5 Marks)
ii. Draw the ogive for gasoline mileage. (5 Marks)

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  • 10 Marks

QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

A business school preparing candidates for professional examinations conducted a mock examination to ascertain the level of preparedness of its candidates in two subjects: Quantitative Techniques in Business (QTB) and Management Information (MI). The table below gives the scores of twelve selected candidates.

Candidates 1 2 3 4 5 6 7 8 9 10 11 12
Score in QTB (x) 35 77 95 28 76 80 90 62 39 65 90 37
Score in MI (y) 50 82 89 58 65 61 84 59 48 53 80 52

Required:
i. Calculate the Spearman’s rank correlation coefficient between xx and yy. (9 Marks)
ii. Comment on the result in (i) above. (1 Mark)

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  • 20 Marks

QTB – Nov 2014 – L1 – SB – Q4 – Forecasting

Analyze sales data using the Least Squares Method and forecast future sales based on the trend.

The sales of PQR Nigeria Plc. in thousands of Naira are listed in the table below for each quarter for years 2005 – 2008.

Sales of PQR in N’000s

Year Quarter 1 Quarter 2 Quarter 3 Quarter 4
2005 22 35 82 37
2006 24 46 81 44
2007 25 40 87 49
2008 29 42 100 55

Required:

a. Calculate the trend in the above data using the Least Squares Method. (12 Marks)
b. Estimate the sales for each quarter using the trend line. (4 Marks)
c. Calculate the percentage variation for each quarter’s actual sales from the estimate obtained in (b) above. (4 Marks)

(Total: 20 Marks)

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  • 20 Marks

QTB – Nov 2014 – L1 – SB – Q3 – Operations Research

Calculate control levels for inventory, expected time for a project, and identify the critical path in a network diagram.

a. Calculate the various control levels from the following data on a given inventory item:

  • Normal usage: 1,600 per day
  • Minimum usage: 1,000 per day
  • Maximum usage: 3,000 per day
  • Lead time: 16 – 20 days
  • EOQ: 40,000
    (9 Marks)

b. If the optimistic, most likely, and pessimistic times are given as 11 days, 15 days, and 18 days respectively, calculate the expected time of the project delivery.
(3 Marks)

c. The network for a small building project is shown below together with the time in days required to complete each task.

Required:

i. List the possible paths together with their durations through the network. (6 Marks)
ii. State the critical path and the project duration. (2 Marks)

(Total: 20 Marks)

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  • 20 Marks

QTB – Nov 2014 – L1 – SB – Q2 – Measures of Dispersion

Compare the risk and return of two investments by calculating mean and standard deviation.

In finance, the standard deviation is frequently used to measure the risk of an investment.
An investor is considering two possible investments A and B. A sample of 10 rates of return is recorded for each investment. These rates of return, given as percentages, are as follows:

Investment A:
4, 6, 6, 5, 4, 5, 8, 5, 5, 8

Investment B:
0, -2, 6, 12, 9, 16, -4, 16, 25, 12

Required:
a. Calculate the mean rate of return for each of the two investments. (6 Marks)
b. Calculate the standard deviation of the rate of return for each of the investments. (6 Marks)
c. Which of the two investments is riskier and why? (8 Marks)

(Total: 20 Marks)

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  • 10 Marks

QTB – Nov 2014 – L1 – SB – Q1b – Mathematics of Business Finance

Determine the total sum of money the Chief Accountant of Zeesco Plc. plans to donate to 4 not-for-profit organisations, given the donations for each organisation.

The Chief Accountant of Zeesco Plc. has a large sum of money which she plans to donate to 4 not-for-profit organisations. She plans to give  of this amount to organisation A. Out of the remaining amount, she plans to give    to organisation B. Also, she intends to give           of the balance to organisation C and the rest to organisation D. If she plans to give 11 million naira to organisation D, how much does she plan to share among these organisations?

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q6b – Data Collection Analysis

Calculate the mode and Pearson's coefficient of skewness for a given distribution of marks.

The table below shows the marks (%) scored in QTB by some candidates who wrote the ICAN Professional examination in May 2016 diet:

Marks % Number of Candidates
20–29 7
30–39 17
40–49 13
50–59 9
60–69 4

If the mean mark is 41.7%, calculate the mode and Pearson’s coefficient of skewness. (10 Marks)

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  • 10 Marks

QTB – Nov 2014 – L1 – SB – Q1a – Mathematics of Business Finance

Determine the cost of calculators and books using a system of linear equations and solve for individual costs.

The cost of purchasing 8 calculators and 10 books is 158 (thousands of naira).
At another instance, the cost of purchasing 15 calculators and 3 books is 123 (thousands of naira).

Required:
i. Use the information above to write down a system of linear equations to describe the given cost scenario. (4 Marks)
ii. Solve the resulting system of equations. (4 Marks)
iii. Find the cost of each calculator and each book. (2 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

i. The laptops that are purchased by a company have 742 diodes with a life span of five months. These diodes fail on a regular basis according to the following probability distribution:

Life (months) 1 2 3 4 5
Probability of failure 0.10 0.30 0.35 0.20 0.05

If the cost of replacing a diode is ₦100, calculate the monthly cost of replacing the diodes as they fail. (4 Marks)

ii. Tadet, a student in the Accountancy Department of a Polytechnic, has the following chances of receiving money from her relatives:

  • 45% chance of receiving ₦5,000 from her sister,
  • 33% chance of receiving ₦8,000 from her brother,
  • 16% chance of receiving ₦11,000 from her aunt,
  • 6% chance of receiving ₦15,000 from her uncle.

Determine if Tadet will be able to buy a gown worth ₦8,000 from the money she is expecting from her relatives. (6 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q5b – Statistics

Calculate the Spearman's rank correlation coefficient between two accountants' rankings of ten banks.

Two Chartered Accountants: X and Y, were requested to rank ten banks A, B, C, D, E, F, G, H, I, J according to their performances during a financial year. X ranked the banks as follows:

  • X’s Rankings: E, B, G, A, C, D, H, F, J, I
  • Y’s Rankings: E, C, A, B, G, H, J, D, F, I

Calculate the Spearman’s rank correlation coefficient between X and Y and interpret your result.

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q5a – Operations Research

Graph linear inequalities and identify the coordinates of the corner points of the shaded area.

Given the following inequalities:

i. Graph them on the same graph sheet using the following scales: On x and y-axes, let 1 cm represent 250 units. (6½ Marks)

ii.

  • Shade the area in which these inequalities hold.
  • Determine the coordinates of the corner points of the above shaded area. (3½ Marks)

 

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q4b – Operations Research

Identify non-basic variables in a transportation model and calculate the probability of a specific event in random disk selection.

i. Given the following initial basic tableau of a transportation problem:

Identify the non-basic variables and compute their corresponding
relative cost coefficients. (4marks)

ii. A bag contains 39,800 white disks and 200 black disks from which
1,000 disks are taken at random. Calculate the probability that the
sample contains 4 black disks. (6marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q4a – Statistics

Calculate the proportion of damaged blocks and the probability of taking a damaged block from a specific lorry using a tree diagram.

a. A fleet of lorries A, B, and C are loaded with blocks meant for a building site.
Lorry A carries 2/5 of all the needed blocks, B carries 3/4 of what lorry A carries, and lorry C carries the rest. Lorries A, B, and C contain 13%, 15%, and 11% damaged blocks, respectively.

By drawing a suitable tree diagram, calculate:
i. The proportion of damaged blocks in the fleet. (8 Marks)

ii. The probability of randomly taking a damaged block from lorry B. (2 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q3b – Data Collection Analysis

Find the regression equation between QTB and FA marks and estimate values.

The table below gives the scores of seven candidates in Quantitative Techniques in Business (QTB) and Financial Accounting (FA) of ICAN Professional Examination:

QTB Marks (y) 50 72 36 64 52 56 80
FA Marks (x) 38 51 19 53 39 38 66

You are required to:
i. Obtain the regression equation if the mark in QTB is regressed on FA. (6 Marks)

ii. Obtain the estimate of mark in QTB, if the mark in FA is 60. (2 Marks)

iii. Obtain the estimate of mark in FA, if the mark in QTB is 75. (2 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q3a – Mathematics

Determine the annual savings required to accumulate a future sum under annuity terms.

A lawyer plans to save a certain amount of money Nx per annum for 5 years on the first day of the year. If the interest rate is 8%, for him to receive N696,910.50, determine x. (10 Marks)

 

 

 

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q2b – Data Collection and Analysis

Determine angles for pie chart representation and complete a project network diagram with project duration.

i. The monthly expenditure (₦’000) of a household on some items are given as follows:

Item Expenditure (₦’000)
Food 50
Transport 25
Utilities 35
Miscellaneous 10

Determine the angle which will represent each item on a pie chart. (6 Marks)

ii. The activities needed to complete a project with their durations (in weeks) are given below:

Activity Preceding Activity Duration (weeks)
A – 4
B – 6
C A 8
D B 12
E B 11
F C, D 9

You are required to draw the activity-on-arrow network diagram for the project and determine the duration of the project. (4 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q2a – Statistics

Probability calculations for dice roll and random sampling in block production.

i. A six-sided and fair die is thrown into the air. What is the probability:

  • Of NOT getting a SIX?
  • That either a THREE, a FOUR, or a FIVE will fall uppermost?
  • Of obtaining an even number?
    (5 Marks)

ii. A block-making factory produces TWO types of blocks: 6-inch and 9-inch. ONE quarter of its output on a particular day are 6-inch blocks, while the remaining three-quarters are 9-inch blocks. If samples of 3 are taken at random, what is the probability of obtaining:

  • One 6-inch block?
  • Two 6-inch blocks?
  • One or two 6-inch blocks?
    (5 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q1b – Data Collection Analysis

Construct a histogram and determine the modal wage from the wage distribution data.

b. The table below shows the weekly wage distribution of artisans in a certain factory:

Weekly Wage (₦’00) Number of Artisans
38 – 47 16
48 – 57 24
58 – 67 41
68 – 77 53
78 – 87 76
88 – 97 118
98 – 107 224
108 – 117 83
118 – 127 15
128 – 137 4

i. Draw a histogram to represent the wage distribution using the scales: On x-axis, let 1 cm represent ₦100; on y-axis, let 1 cm represent 10 artisans. (4 Marks)

ii. Deduce the modal weekly wage from the histogram. (2½ Marks)

iii. Use the appropriate formula to calculate the modal weekly wage. (3½ Marks)

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