Subject: QUANTITATIVE TOOLS IN BUSINESS

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QTB – MAY 2016 – L1 – SA – Q14 – Statistics

Calculate probability of specific outcomes when tossing a coin and rolling a die

Question

If a coin and an unbiased die are tossed together, what is the probability of
obtaining a tail and a number greater than 3?

A. 0.25
B. 0.33
C. 0.35
D. 0.50
E. 0.75

Answer

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Tags: Coin Toss, Dice Roll, Probability Calculation
Level: Level 1

Topic: Statistics
Series: MAY 2016

QT – May 2016 – L1 – Q7 – Mathematics of Business Finance

Construct an amortization schedule for a loan of GH¢3,000 over 12 years with an annual interest rate of 2%.

Question

A loan of GH¢3,000 at an effective annual interest rate of i = 12% is amortized by means of 12 annual payments, beginning a year after the loan is taken.

Hint: The schedule should have the following columns: Payment, Interest Due, Principal Repaid, and Outstanding Balance.

Required:
Construct an amortization schedule.

Answer

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Tags: Compound Interest, Effective Interest, Loan amortization, Schedules
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2016

QT – May 2016 – L1 – Q6b – Data Collection | Measures of Central Tendency

Compute the sample mean, variance, standard deviation, covariance, and correlation for the given data.

Question

b) Use the sample data below to answer the following questions:

Required:
i) Calculate the sample mean, variance, and standard deviation for . (5 marks)
ii) Calculate the sample mean, variance, and standard deviation for $Y$ . (5 marks)
iii) Calculate the sample covariance between and . (3 marks)
iv) Calculate the sample correlation between and $Y$ . (3 marks)

Answer

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Tags: Correlation, Covariance, Sample Mean, Standard Deviation, Variance
Level: Level 1

Topic: Data Collection, Measures of Central Tendency
Series: MAY 2016

QT – May 2016 – L1 – Q6a – Data Collection

Distinguish between a population and a sample, and between a statistic and a parameter.

Question

a)
i) Distinguish between a Sample and a Population. (2 marks)
ii) Distinguish between a Statistic and a Parameter. (2 marks)

Answer

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Tags: Data collection, Parameter, Population, Sample, Statistic
Level: Level 1

Topic: Data Collection
Series: MAY 2016

QT – May 2016 – L1 – Q5b – Equalities and Inequalities

Solve simultaneous equations representing a word problem about total cash in GHS 10 and GHS 20 notes.

Question

Mini has some GH¢10 notes and some GH¢20 notes. If she has 273 notes worth a total of GH¢4,370:

Required:
i) Write down the system of linear equations. (5 marks)
ii) Solve the system of linear equations. (5 marks)

Answer

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Tags: Algebra, Linear Equations, Simultaneous Equations, Word Problem
Level: Level 1

Topic: Equalities and Inequalities
Series: MAY 2016

QT – May 2016 – L1 – Q5a – Mathematics of Business Finance

Calculate the total cost, average cost, and marginal cost of producing 5000 items, and determine the production level for the lowest average cost.

Question

a) If the total cost (in Ghana cedis) of producing $x$ items is given by the function

Required:
i) Calculate the total cost, average cost, and marginal cost of producing 5000 items. (6 marks)
ii) Determine the production level at which the average cost will be the lowest. (4 marks)

Answer

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Tags: Average Cost, Cost Functions, Marginal Cost, Optimization
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2016

QT – May 2016 – L1 – Q4 – Probability

Determine percentages of receipts using normal distribution and calculate mean and standard deviation based on given conditions.

Question

a) Receipts at a particular depot have amounts which follow the Normal distribution with a mean of GH¢103.60 and a standard deviation of GH¢8.75.

Required:
i) Determine the percentage of receipts over GH¢120.05.
ii) Determine the percentage of receipts below GH¢92.75.
iii) Determine the percentage of receipts between GH¢83.65 and GH¢117.60.
iv) Determine the receipts amount such that approximately 25 percent of receipts are greater.
v) Above what amount will 90 percent of receipts lie?

b) If 10.56 percent of receipts have an amount above GH¢110.05 and 4.01 percent of receipts have an amount above GH¢120.05.

Required:
Calculate the mean and standard deviation of the receipts assuming that they are normally distributed.

Answer

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Tags: Mean, Normal distribution, Probability, Receipts, Standard Deviation, Z-scores
Level: Level 1

Topic: Probability
Series: MAY 2016

QT – May 2016 – L1 – Q3 – Probability

Calculate the probabilities of various outcomes in a card drawing scenario, including conditional probability based on drawing a red card.

Question

a) If from a normal pack of 52 cards, consisting of four suites each of 13 cards, one card is randomly selected:

Required:

Calculate the probabilities of selecting the following:

i) An ace
ii) A club
iii) An ace or a club
iv) The ace of clubs
v) A picture card (i.e. a jack, queen or king)
vi) A red card
vii) A red king
viii) A red picture card

b) Given that a card selected is red, calculate the probability that it is a picture card.

Answer

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Tags: Card Shuffle, Conditional Probability, Mutually Exclusive Events, Probability
Level: Level 1

Topic: Probability
Series: MAY 2016

QT – Nov 2017 – L1 – Q7b – Mathematics of Business Finance

Calculate the future value of a depreciated vehicle and the amount required in a sinking fund to replace it.

Question

Alpha Transport Company buys a vehicle for GH¢265,000. The value of the vehicle depreciates on a reducing balance basis at 17% per annum. The company plans to replace this vehicle in 5 years’ time, and they expect the price of a new vehicle to increase annually by 12%.

Required:
i) Calculate the book value of the vehicle in five years’ time. (3 marks)
ii) Determine the amount of money needed in the sinking fund for the company to be able to afford a new vehicle in five years’ time. (3 marks)
iii) Calculate the required monthly deposits if the sinking fund earns an interest rate of 11% per annum compounded monthly. (3 marks)

Answer

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Tags: Compound Interest, Depreciation, Sinking Fund
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2017

QT – Nov 2017 – L1 – Q7a – Mathematics of Business Finance

Determine the timeline for savings and calculate the time required to reach a target amount with compound interest.

Question

Every Monday, Kwei puts GH¢30 into a savings account at the Ring Bank, which accrues interest of 6.92% per annum compounded weekly.

Required:
i) Draw a cash flow timeline showing the payments, the interest rate, and the present values for the first four payments. (3 marks)
ii) Determine how long it will take Kwei’s account to reach a balance of GH¢4,397.53. Convert your answer into the number of years and days to the nearest integer. (6 marks)
iii) Determine how much interest Kwei will receive from the bank during the period of his investment.

Answer

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Tags: Compound Interest, Present Value, Savings
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2017

QT – May 2019 – L1 – Q2b – Mathematics of Business Finance

Calculate NPV and IRR for two machines and determine which machine yields a better return.

Question

BonBone Company Ltd wants to make a decision on which of the two machines to purchase. Each will involve a GH¢10,000 investment. The expected net incremental cash flows are given by the table below:

Year	Machine I (GH¢)	Machine II (GH¢)
1	5,000.00	2,000.00
2	4,000.00	3,000.00
3	2,000.00	5,000.00
4	2,000.00	4,000.00

Required:

i) If the company’s cost of capital is 10%, calculate the Net Present Value (NPV) of Machine I and Machine II and determine which machine should be purchased for higher returns. (8 marks)

ii) If the initial investment for Machine I is changed to GH¢4,000 and Machine II is changed to GH¢2,000, calculate the Internal Rate of Return (IRR) for Machine I and Machine II. (6 marks)

iii) If the IRRs in (ii) above are to be used as the basis of selection, determine which machine should be purchased for higher returns. (2 marks)

Answer

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Tags: Capital Budgeting, Discounting, Internal Rate of Return, Investment Decision, Net Present Value

Topic: Mathematics of Business Finance
Series: MAY 2019

QT – May 2019 – L1 – Q2a – Mathematics of Business Finance

Distinguish between IRR and NPV, and evaluate investment decisions using NPV and IRR.

Question

Distinguish between Internal Rate of Return and Net Present Value. (4 marks)

Answer

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Tags: Capital Budgeting, Discounting, Internal Rate of Return, Investment Decision, Net Present Value
Level: Level 1

Topic: Mathematics of Business Finance
Series: MAY 2019

QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

Question

The number of clients who consulted Tsoo Consult within a period of three years were recorded as follows:

Year	Quarter 1	Quarter 2	Quarter 3	Quarter 4
1	75	70	75	80
2	95	85	80	65
3	100	105	115	90

Required:
a) Assuming a 4 quarterly cycle, calculate the centred trend values for the data by moving average method. (4 marks)

b) Using (a) above and the multiplicative model, calculate the average seasonal variations. (5 marks)

c) Using (b) above, calculate the adjusted average seasonal variations for the data. (5 marks)

d) Using the trend and the adjusted average seasonal variation, forecast the number of clients for Year 4 based on the multiplicative model. (6 marks)

Answer

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Tags: Forecasting, Moving Averages, Multiplicative Model, Seasonal Variation, Time series
Level: Level 1

Topic: Forecasting
Series: MAY 2019

QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

Question

The following data gives how much 10 students of ICAG spend on TroTro to the Institute and food weekly:

Food (x)	10	12	14	16	18	20	22	24	26	28
TroTro (y)	25	24	22	20	19	17	13	12	11	10

Required:

a) Using a graph paper, construct a scatter diagram of the data.
(4 marks)

b) Determine the correlation coefficient.
(4 marks)

c) Calculate the coefficient of determination of the data and interpret its value.
(4 marks)

d) Determine the regression line of $y$ on $x$ , and interpret the coefficient.
(8 marks)

Answer

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Tags: Coefficient of Determination, Correlation Coefficient, Regression Line, Scatter Diagram
Level: Level 1

Topic: Forecasting
Series: MAY 2017

QT – May 2017 – L1 – Q6b – Probability

Determine the probabilities of specific outcomes when tossing three fair coins.

Question

If three fair coins are tossed:

Required:

i) Determine the probability of getting two heads and a tail.
(3.5 marks)

ii) Determine the probability of getting three tails.
(3 marks)

Answer

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Tags: Coin Toss, Conditional Probability, Probability
Level: Level 1

Topic: Probability
Series: MAY 2017

QT – May 2017 – L1 – Q6a – Probability

Calculate probabilities from a tree diagram based on people's chocolate preferences and eye color.

Question

Consider people’s preferences in terms of chocolate and their eye color, presented as a probability tree diagram below:

30% of people have brown eyes, 40% have green eyes, and the remaining have blue eyes.
70% prefer milk chocolate, 10% prefer white chocolate, and the remaining prefer plain chocolate.

Using the tree diagram above, calculate the probability that a person:

i) Prefers plain chocolate and has brown eyes.
(1.5 marks)

ii) Prefers milk chocolate and has brown eyes.
(1.5 marks)

iii) Prefers white chocolate and has brown eyes.
(1.5 marks)

iv) Prefers plain chocolate and has green eyes.
(1.5 marks)

v) Prefers milk chocolate and has green eyes.
(1.5 marks)

vi) Prefers white chocolate and has green eyes.
(1.5 marks)

vii) Prefers plain chocolate and has blue eyes.
(1.5 marks)

viii) Prefers milk chocolate and has blue eyes.
(1.5 marks)

ix) Prefers white chocolate and has blue eyes.
(1.5 marks)

Answer

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Tags: Conditional Probability, Probability, Tree Diagram
Level: Level 1

Topic: Probability
Series: MAY 2017

QT – May 2017 – L1 – Q5 – Measures of Central Tendency

Create a frequency table and compute measures of central tendency and dispersion from given data.

Question

The mileages recorded for a sample of company vehicles during a given week gave the following data:

Required:

a) Draw the frequency table of this data, given a class size of 5.
(6 marks)

b) Determine the mean, median, and mode for the data and comment on the distribution.
(6 marks)

c) Compute the quartile deviation.
(4 marks)

d) Determine the standard deviation for the data.
(4 marks)

Answer

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Tags: Frequency Distribution, Mean, Median, Mode, Quartile Deviation, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: MAY 2017

QT – May 2017 – L1 – Q4b – Linear Programming

Formulate a linear programming model for maximizing profit.

Question

Managers within a subsidiary company in a conglomerate want to know how to maximize profit from two types of products, X and Y. Each product X requires one hour of labor and six liters of molding material, whereas each product Y requires two hours of labor and five liters of molding material. The total labor hours available for each week is 40, and the total amount of molding material each week is 150 liters. The profit contribution from product X is GH¢20 and from product Y is GH¢30.

Required:

Formulate the linear programming model for the problem.

Answer

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Tags: Linear Programming, Model Formulation, Profit Maximization
Level: Level 1

Topic: Linear Programming
Series: MAY 2017

QT – May 2017 – L1 – Q4a – Linear Programming

Graphically represent constraints and determine the optimum solution.

Question

A particular linear programming problem is formulated as follows:

Subject to the constraints:

Required:

i) Draw these constraints on the same graph paper.

ii) Determine the optimum solution.

Answer

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Tags: Constraints, Graphical Solution, Linear Programming
Level: Level 1

Topic: Linear Programming
Series: MAY 2017

QT – May 2017 – L1 – Q3b – Elements of Calculus

Use integration to calculate total cost from a marginal cost function with a given fixed cost.

Question

At the Zee manufacturing company, the marginal cost for producing $x$ gears, measured in hundreds, is:

If the fixed cost (the cost of producing zero items) is GH¢3000:

Required:

Determine the total cost for manufacturing 5000 gears.
(11 marks)

Answer

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Tags: Fixed Cost, Integration, Marginal Cost, Total Cost
Level: Level 1

Topic: Elements of Calculus
Series: MAY 2017

Subject: QUANTITATIVE TOOLS IN BUSINESS

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QTB – MAY 2016 – L1 – SA – Q14 – Statistics

Calculate probability of specific outcomes when tossing a coin and rolling a die

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QT – May 2016 – L1 – Q7 – Mathematics of Business Finance

Construct an amortization schedule for a loan of GH¢3,000 over 12 years with an annual interest rate of 2%.

You're reporting an error for "QT – May 2016 – L1 – Q7 – Mathematics of Business Finance"

QT – May 2016 – L1 – Q6b – Data Collection | Measures of Central Tendency

Compute the sample mean, variance, standard deviation, covariance, and correlation for the given data.

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QT – May 2016 – L1 – Q6a – Data Collection

Distinguish between a population and a sample, and between a statistic and a parameter.

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QT – May 2016 – L1 – Q5b – Equalities and Inequalities

Solve simultaneous equations representing a word problem about total cash in GHS 10 and GHS 20 notes.

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QT – May 2016 – L1 – Q5a – Mathematics of Business Finance

Calculate the total cost, average cost, and marginal cost of producing 5000 items, and determine the production level for the lowest average cost.

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QT – May 2016 – L1 – Q4 – Probability

Determine percentages of receipts using normal distribution and calculate mean and standard deviation based on given conditions.

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QT – May 2016 – L1 – Q3 – Probability

Calculate the probabilities of various outcomes in a card drawing scenario, including conditional probability based on drawing a red card.

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QT – Nov 2017 – L1 – Q7b – Mathematics of Business Finance

Calculate the future value of a depreciated vehicle and the amount required in a sinking fund to replace it.

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QT – Nov 2017 – L1 – Q7a – Mathematics of Business Finance

Determine the timeline for savings and calculate the time required to reach a target amount with compound interest.

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QT – May 2019 – L1 – Q2b – Mathematics of Business Finance

Calculate NPV and IRR for two machines and determine which machine yields a better return.

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QT – May 2019 – L1 – Q2a – Mathematics of Business Finance

Distinguish between IRR and NPV, and evaluate investment decisions using NPV and IRR.

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QT – May 2019 – L1 – Q1a – Forecasting

Calculate centered trend values using moving average, determine seasonal variations, adjust variations, and forecast future clients using a multiplicative model.

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QT – May 2017 – L1 – Q7 – Forecasting

Construct a scatter diagram and compute correlation, regression line, and coefficient of determination from given data.

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QT – May 2017 – L1 – Q6b – Probability

Determine the probabilities of specific outcomes when tossing three fair coins.

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QT – May 2017 – L1 – Q6a – Probability

Calculate probabilities from a tree diagram based on people's chocolate preferences and eye color.

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QT – May 2017 – L1 – Q5 – Measures of Central Tendency

Create a frequency table and compute measures of central tendency and dispersion from given data.

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QT – May 2017 – L1 – Q4b – Linear Programming

Formulate a linear programming model for maximizing profit.

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QT – May 2017 – L1 – Q4a – Linear Programming

Graphically represent constraints and determine the optimum solution.

You're reporting an error for "QT – May 2017 – L1 – Q4a – Linear Programming"

QT – May 2017 – L1 – Q3b – Elements of Calculus

Use integration to calculate total cost from a marginal cost function with a given fixed cost.

You're reporting an error for "QT – May 2017 – L1 – Q3b – Elements of Calculus"

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