a) The normal distribution is a probability distribution which usually applies to continuous variables.
Required:
i) State FOUR (4) properties of the Normal Distribution.                                                                                                  (4 marks)

ii) State TWO (2) examples of phenomena which closely follow a Normal Distribution.                                          (2 marks)

b) In a study commissioned by Ofo Stores, the researcher examined the spending habits of the residents of Kojokrom. He found the spending habits to be normally distributed with mean of GH¢700 and standard deviation of GH¢70.
Required:
a) Determine the probability that a resident selected at random spends:
i) Less than GH¢620                                                                                                                                                      (3 marks)

ii) More than GH¢1,000                                                                                                                                                 (3 marks)

iii) Between GH¢800 and GH¢900                                                                                                                                (4 marks)

b) Calculate the amount:
i) Above which 80% of the residents will spend in a week.                                                                                          (2 marks)

ii) Below which 30% of the residents will spend in a week.                                                                                          (2 marks)

a) When is the mode preferred to the mean or the median as a measure of central tendency?                                           (5 marks)

b) BomBo, a market researcher at a major African Automobile Company (African Moon) classified households by car ownership. The relative frequencies of households for each category of ownership are shown below:

Required:
i) Calculate the expected value of the random variable.                                                                                                    (4 marks)

ii) Calculate the standard deviation of the random variable.                                                                                              (4 marks)

iii) Draw Relative Percentage Histogram for the data.                                                                                                       (4 marks)

iv) Using (i)-(iii) comment on the distribution of the data.                                                                                                 (3 marks)

After the collapse of a Savings and Loans Company, depositors who were able to recover funds lodged with the company are seeking alternative avenues of investment. You have been called upon to advise the following clients on investment decisions they have to make.
a) Kwabena was able to recover GH¢150,000 out of GH¢200,000 invested in the Savings and Loans Company. How much money should he invest at a return of 6% per annum so as to earn an annual income of GH¢15,000 for a period of 10 years? (10 marks)

b) Kasuli, a Marketing Executive who could not recover any amount out of his investment decided to take a mortgage at an interest rate of 15% over a 20 year term. If his income is enough to enable him to pay GH¢1,400 per month, what is the maximum amount he can borrow?                                                                                                                                    (10 marks)

a) What is a Stationary Point of a differentiable function of one variable?                                                                        (2 marks)

b) 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=300−0.02q. 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)

c) Due to changes in market conditions, the company finds the demand q, in thousands, for their kente strips to be at a price of GH¢p (p Ghana Cedis).
Required:
i) Determine the elasticity of demand when the price is GH¢5 and when the price is GH¢15 per kente strip.                  (6 marks)

ii) Comment on your results in (i).                                                                                                                                      (2 marks)

a) Explain the term Coefficient of Correlation in forecasting.                                                                                            (3 marks)

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

Required:
i) Determine how many errors a student would make in the examination if he studied for 280 minutes.                          (8 marks)

ii) Determine the expected change in number of errors if there is 1 minute change in study time.                                    (2 marks)

iii) Compute Pearson Product Moment Correlation coefficient between study time and number of errors made.            (5 marks)

iv) Compute the coefficient of determination between study time and number of errors made and comment on your results.     (2 marks)

a) Sketch a scatter graph for two variables (dependent and independent variables) that represents:
i) Perfect positive correlation between the variables.                                                                                                          (1 mark)

ii) Perfect negative correlation between the variables.                                                                                                        (1 mark)

b) The secretariat of an association of industries gathered the following data from a random sample of member firms that produce similar products:

Required:
i) Compute the Pearson’s product moment correlation coefficient for the data.                                                                 (6 marks)

ii) Hence, compute the coefficient of determination.                                                                                                          (2 marks)

iii) Comment on your answer in (ii).                                                                                                                                   (2 marks)

iv) Compute Spearman’s rank correlation coefficient for the data and comment on your answer.                                     (8 marks)

a)
i) Distinguish between measures of central tendency and measures of dispersion (or variation)                                    (2 marks)

ii) State TWO examples of measures of central tendency.                                                                                                   (1 mark)

iii) State TWO examples of measures of measures of dispersion (or variation).                                                                 (1 mark)

b) The table below shows the range of bi-weekly income of a sample of 50 accountants of a multi-national accounting firm:

Required:
i) Compute all the THREE measures of central tendency of the range of income and comment on the distribution.       (8 marks)

ii) Compute the coefficient of variation of the range of income of the accountants.                                                          (7 marks)

iii) Interpret your answer in (ii) above.                                                                                                                                 (1 mark)

Kofy Addo decided to start saving money for his future. At the end of each month he deposited GH¢500 into an account at Trust Bank, which earned an interest rate of 9% per annum compounded monthly.
Required:
i) Determine the balance of Kofy Addo’s account after 20 years.                                                                                     (4 marks)

ii) Calculate the amount deposited into the account over the 20 year period.                                                                   (2 marks)

iii) Calculate how much interest he earned over the 20 year period.                                                                                 (2 marks)

iv) Calculate the effective annual rate of interest.                                                                                                              (2 marks)

Kofy Addo invested GH¢4,000 into his bank account at the beginning of every year for four years. The bank paid interest at 8% compounded annually for the first four years. Thereafter, the interest rate changed to 8.35% but Kofy Addo did not make any more deposits. At the end of the sixth year he withdrew GH¢5000.
Required:
i) Calculate the size of the investment at the end of the sixth year, before the withdrawal.                                               (5 marks)

ii) Calculate the size of the investment after the withdrawal in the sixth year.                                                                   (2 marks)

iii) Calculate the balance in the account after the eighth year.                                                                                            (3 marks)

The quarterly unit sales of electronic items of a retail company for the last three years are as follows:

Required:
i) Calculate a centred three moving average of the unit sales.                                                                                           (3 marks)

ii) Calculate the trend using a centred four-quarterly moving average.                                                                             (4 marks)

iii) Calculate the four seasonal variations using (ii) and the multiplicative model.                                                           (7 marks)

iv) Forecast the number of unit sales for the year 2016 using the multiplicative model.                                                   (4 marks)

v) Comment on your answer in (iv).                                                                                                                                   (2 marks)