QUANTITATIVE TOOLS IN BUSINESS – Page 10

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 2015 – L1 – Q4 – Measures of Central Tendency

Discuss the relationships between mean, median, and mode in non-symmetric distributions and calculate percentages using a normal distribution.

Question

(a) State the relationships between the mean, median, and mode in a non-symmetric distribution. (5 Marks)

(b) A large departmental store, BOBO, has analyzed the monthly amount spent by its credit card customers and found that it is normally distributed with a mean of GHC 100 and a standard deviation of GHC 15.

Required:
Determine the percentage of people who will spend:
(i) Over GHC 130 (2 Marks)
(ii) Over GHC 120 (2 Marks)
(iii) Below GHC 70 (2 Marks)
(iv) Between GHC 100 and GHC 130 (2 Marks)
(v) Between GHC 115 and GHC 130 (2 Marks)
(vi) The minimum amount spent by the top 10% of customers (2.5 Marks)
(vii) The minimum amount spent by the top 3% of customers (2.5 Marks)

Answer

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Tags: Mean, Median, Mode, Non-symmetric distribution, Normal distribution, Probability
Level: Level 1

Topic: Measures of Central Tendency
Series: NOV 2015

QT – Nov 2015 – L1 – Q3 – Forecasting

Calculate the regression line for maize demand and forecast demand for the first three months of the next year using regression analysis.

Question

The monthly demand for maize (in hundreds of bags) for the last year in Bosua Market is shown below:

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Demand	42	43	40	44	50	47	53	49	54	57	63	60

Required:
(a) Calculate the regression line $y = a + b x$ for the data. (9 Marks)

(b) Using the regression line in (a), determine the forecast for next year:
(i) January, (1 Mark)
(ii) February, (1 Mark)
(iii) March. (1 Mark)

Answer

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Tags: Demand forecast, Forecasting, Regression Analysis, Standard error, Trend Analysis
Level: Level 1

Topic: Forecasting
Series: NOV 2015

QT – Nov 2015 – L1 – Q2 – Probability

Construct a decision tree and calculate the expected monetary value for Jodoo Company Ltd’s expansion options.

Question

Jodoo Company Ltd had a new, large order for its product and thinks this may herald an expansion of the market and thus its sales and profits. Jodoo Ltd could move the factory to a new and larger site (cost: GHS 1 million), expand the existing factory (cost: GHS 0.25 million), or meet the new order by overtime (cost: GHS 0.08 million).

Three likely sales increase scenarios were proposed:

40% increase in sales with a probability of 0.2
10% increase in sales with a probability of 0.6
0% increase in sales with a probability of 0.2

The expected profits under each option are:

Sales Increase %	New Factory (GHS million)	Expanded Factory (GHS million)	Overtime (GHS million)
40%	6	3.5	1.5
10%	2.5	2.5	1.5
0%	0	0	0

Required:
(i) Construct a decision tree to represent the various scenarios of expansion. (6 Marks)

(ii) Calculate the expected monetary value (EMV) of each node of your tree. (8 Marks)

(iii) Advise the company on how to react to this opportunity. (6 Marks)

Answer

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Tags: Business decision, Decision tree, Expected Monetary Value, Payoff table, Probability
Level: Level 1

Topic: Probability
Series: NOV 2015

QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

Question

Quarterly sales of a Golden Tree Chocolate Bar at a popular mall in KoKoLand City are given as follows:

YEAR	QUARTER 1	QUARTER 2	QUARTER 3	QUARTER 4
1	1260	756	588	1596
2	1352	966	579	2028
3	1786	920	865	2273

Required:
(i) Calculate the trend in the series using a 4-point centered moving average method. (4 Marks)

(ii) Using (i), calculate the Average Seasonal Variation based on the Additive Model of Time Series analysis. (4 Marks)

(iii) Using the values in (ii), determine the Adjusted Average Seasonal Variation for the Time Series Data. (4 Marks)

(iv) Prepare Seasonal Adjusted Forecast for Year 4 using the Additive Model. (4 Marks)

Answer

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Tags: Additive model, Forecasting, Seasonal Variation, Time series, Trend Analysis
Level: Level 1

Topic: Forecasting
Series: NOV 2015

QT – Nov 2015 – L1 – Q1a – Forecasting

State the four factors commonly found in time series data.

Question

State the four (4) factors which may be present in a Time Series Data. (4 Marks)

Answer

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Tags: Cyclical, Factors, Forecasting, Random, Seasonal, Time series, Trend
Level: Level 1

Topic: Forecasting
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

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%.

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.

QT – May 2016 – L1 – Q6a – Data Collection

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

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.

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.

QT – May 2016 – L1 – Q4 – Probability

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

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.

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.

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.

QT – Nov 2015 – L1 – Q4 – Measures of Central Tendency

Discuss the relationships between mean, median, and mode in non-symmetric distributions and calculate percentages using a normal distribution.

QT – Nov 2015 – L1 – Q3 – Forecasting

Calculate the regression line for maize demand and forecast demand for the first three months of the next year using regression analysis.

QT – Nov 2015 – L1 – Q2 – Probability

Construct a decision tree and calculate the expected monetary value for Jodoo Company Ltd’s expansion options.

QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

QT – Nov 2015 – L1 – Q1a – Forecasting

State the four factors commonly found in time series data.

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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.

You're reporting an error for "QT – May 2016 – L1 – Q5b – Equalities and Inequalities"

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.

You're reporting an error for "QT – May 2016 – L1 – Q4 – Probability"

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 2015 – L1 – Q4 – Measures of Central Tendency

Discuss the relationships between mean, median, and mode in non-symmetric distributions and calculate percentages using a normal distribution.

You're reporting an error for "QT – Nov 2015 – L1 – Q4 – Measures of Central Tendency"

QT – Nov 2015 – L1 – Q3 – Forecasting

Calculate the regression line for maize demand and forecast demand for the first three months of the next year using regression analysis.

You're reporting an error for "QT – Nov 2015 – L1 – Q3 – Forecasting"

QT – Nov 2015 – L1 – Q2 – Probability

Construct a decision tree and calculate the expected monetary value for Jodoo Company Ltd’s expansion options.

You're reporting an error for "QT – Nov 2015 – L1 – Q2 – Probability"

QT – Nov 2015 – L1 – Q1b – Forecasting

Calculate the trend, average seasonal variation, and forecast for Year 4 using a 4-point centered moving average method for Golden Tree Chocolate Bar sales.

You're reporting an error for "QT – Nov 2015 – L1 – Q1b – Forecasting"

QT – Nov 2015 – L1 – Q1a – Forecasting

State the four factors commonly found in time series data.

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