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 – Nov 2018 – L1 – Q2b – Elements of Calculus

Determine the price and quantity that maximize revenue and profit, and compute the maximum profit for Renes Trading Company.

Question

Renes Trading Company sells $q$ kente strips per month at $p$ Ghana Cedis per kente strip. The demand function for kente strips is given by $p = 300 - 0.02 q$ . The kente strips cost GH¢30 per strip to manufacture. There are fixed costs of GH¢9,000 per month.

Required:
(i) Determine the price per kente strip that will maximize revenue. (4 marks)
(ii) Determine the quantity where profit is maximized. (4 marks)
(iii) Calculate the maximum profit. (2 marks)

Answer

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Tags: Differentiation, Elasticity of Demand, Profit Maximization, Revenue Maximization
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2018

QT – Nov 2018 – L1 – Q2a – Elements of Calculus

Define the stationary point of a differentiable function of one variable.

Question

What is a Stationary Point of a differentiable function of one variable?

Answer

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Tags: Differentiation, Maximum and Minimum, Stationary Point
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2018

QT – Nov 2018 – L1 – Q1b – Forecasting

Determine the number of errors a student would make after 280 minutes of study and the expected change in errors for a 1-minute change.

Question

The study time in minutes and the number of errors on a mock examination paper made by ten (10) ICAG students are given below:

Student	1	2	3	4	5	6	7	8	9	10
Study Time (X)	90	100	130	150	180	200	220	300	350	400
Errors (Y)	25	28	20	20	15	12	13	10	8	6

(i) Determine how many errors a student would make in the examination if he studied for 280 minutes.

(ii) Determine the expected change in the number of errors if there is a 1-minute change in study time.

Answer

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Tags: Errors Prediction, Regression Analysis, Study Time
Level: Level 1

Topic: Forecasting
Series: NOV 2018

QT – Nov 2018 – L1 – Q1a – Forecasting

Explain the term coefficient of correlation in forecasting.

Question

Explain the term Coefficient of Correlation in forecasting.

Answer

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Tags: Coefficient of Correlation, Forecasting, Regression
Level: Level 1

Topic: Forecasting
Series: NOV 2018

QT – Nov 2015 – L1 – Q7b – Elements of Calculus

Determine the number of TV sets a manufacturer should produce to maximize profit and calculate the maximum profit.

Question

A TV manufacturer finds that he can sell $x$ units per week at a price $p = 250 - 0.5 x$ each. His cost of production of $x$ TV sets per week is given by $C = 240 + 2 x$ .

Required:
(i) Determine how many sets per week he should produce to maximize his profit. (5 Marks)
(ii) Determine the maximum profit. (2 Marks)

Answer

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Tags: Marginal Cost, Marginal Revenue, Production, Profit Maximization, TV Sets
Level: Level 1

Topic: Elements of Calculus
Series: NOV 2015

QT – Nov 2015 – L1 – Q7a – Probability

Explain five key decision-making terms including Maximax rule and Expected Monetary Value.

Question

Explain the following terms in decision making:
(i) Maximax Rule
(ii) Maximin Rule
(iii) Expected Monetary Value
(iv) Payoff Table
(v) Expected Value of Perfect Information

Answer

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Tags: Decision Making, Expected Monetary Value, Expected Value of Perfect Information, Maximax Rule, Maximin Rule, Payoff table
Level: Level 1

Topic: Probability
Series: NOV 2015

QT – Nov 2015 – L1 – Q6b – Measures of Central Tendency

Compute the mean, median, mode, and variance from data on textbook expenses.

Question

You have been given the responses of 18 ICAG students to a question on how much they have spent on textbooks in the last month:

Required:
(i) Compute the mean, median, and mode. Comment on the distribution of the responses.
(ii) Compute the inter-quartile deviation, mean deviation, and the standard deviation. Comment on your results.

Answer

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Tags: Inter-quartile Deviation, Mean, Mean Deviation, Median, Mode, Standard Deviation
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2015

QT – Nov 2015 – L1 – Q6a – Measures of Central Tendency

Calculate the geometric mean of the rates of return for an investment on the Ghana Stock Exchange.

Question

Calculate the geometric mean of the following rates of return for an investment on the Ghana Stock Exchange:
0.50, 0.30, -0.50, -0.25

Answer

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Tags: Geometric Mean, Ghana Stock Exchange, Investment, Rates of Return
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2015

QT – Nov 2015 – L1 – Q5c – Mathematics of Business Finance

Calculate the accumulated value of GHS 2000 over 5 years at 16% compounded quarterly, monthly, annually, semi-annually, and continuously.

Question

Calculate the accumulated value of GHS 2000 for 5 years at 16% compounded:
(i) Quarterly
(ii) Monthly
(iii) Annually
(iv) Semi-annually
(v) Continuously

Answer

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Tags: Accumulated value, Compound Interest, Continuous compounding, Monthly compounding, Quarterly Compounding
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2015

QT – Nov 2015 – L1 – Q5a – Mathematics of Business Finance

Calculate the sum of infinite geometric progressions for two sequences.

Question

Calculate the sum of the infinite geometric progressions:

(i)

(ii)

Answer

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Tags: Accumulated value, Compound Interest, Geometric progression, Investment
Level: Level 1

Topic: Mathematics of Business Finance
Series: NOV 2015

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.

You're reporting an error for "QT – May 2016 – L1 – Q6b – Data Collection | Measures of Central Tendency"

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.

You're reporting an error for "QT – May 2016 – L1 – Q5a – Mathematics of Business Finance"

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.

You're reporting an error for "QT – May 2016 – L1 – Q3 – Probability"

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.

You're reporting an error for "QT – Nov 2017 – L1 – Q7b – Mathematics of Business Finance"

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.

You're reporting an error for "QT – Nov 2017 – L1 – Q7a – Mathematics of Business Finance"

QT – Nov 2018 – L1 – Q2b – Elements of Calculus

Determine the price and quantity that maximize revenue and profit, and compute the maximum profit for Renes Trading Company.

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QT – Nov 2018 – L1 – Q2a – Elements of Calculus

Define the stationary point of a differentiable function of one variable.

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QT – Nov 2018 – L1 – Q1b – Forecasting

Determine the number of errors a student would make after 280 minutes of study and the expected change in errors for a 1-minute change.

You're reporting an error for "QT – Nov 2018 – L1 – Q1b – Forecasting"

QT – Nov 2018 – L1 – Q1a – Forecasting

Explain the term coefficient of correlation in forecasting.

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QT – Nov 2015 – L1 – Q7b – Elements of Calculus

Determine the number of TV sets a manufacturer should produce to maximize profit and calculate the maximum profit.

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QT – Nov 2015 – L1 – Q7a – Probability

Explain five key decision-making terms including Maximax rule and Expected Monetary Value.

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QT – Nov 2015 – L1 – Q6b – Measures of Central Tendency

Compute the mean, median, mode, and variance from data on textbook expenses.

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QT – Nov 2015 – L1 – Q6a – Measures of Central Tendency

Calculate the geometric mean of the rates of return for an investment on the Ghana Stock Exchange.

You're reporting an error for "QT – Nov 2015 – L1 – Q6a – Measures of Central Tendency"

QT – Nov 2015 – L1 – Q5c – Mathematics of Business Finance

Calculate the accumulated value of GHS 2000 over 5 years at 16% compounded quarterly, monthly, annually, semi-annually, and continuously.

You're reporting an error for "QT – Nov 2015 – L1 – Q5c – Mathematics of Business Finance"

QT – Nov 2015 – L1 – Q5a – Mathematics of Business Finance

Calculate the sum of infinite geometric progressions for two sequences.

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