a) The following table shows the quarterly index of industrial production of a certain product over three years from the year of 2016 to the year of 2018, Quarter Year First Second Third Fourth 2016 115 116 107 116 2017 116 117 109 1 18 2018 115 119 114 127 (i) Obtain the trend values using suitable moving average method. (6 marks) (ii) Calculate the average quarterly variations using the additive model. (6 marks) (iii) Forecast the production index for the first quarter of the year 2019. (3 marks) b) Hani has to pay RM880 at the end of every month for 84 months to settle a car loan with an interest rate of 6% per annum compounded monthly. Find (i) the original value of the loan; (3 marks) (ii) the total interest she needs to pay. (1 mark) c) A project requires an initial investment of RM225.000 and is expected to generate the following net cash inflows: Year Net cash flow (RM) 95,000 80,000 WN 60,000 4 55,000 Compute the net present value (NPV) of the project if the minimum desired rate of return is 12% per annum. Should the investment be given a green light? (6 marks)Question 2 a) The starting salaries of fresh graduates follow a Normal distribution with a mean of RM2350 and a standard deviation of RM400. What is the probability that a randomly selected fresh graduate will have a starting salary of (1) more than RM2200? (4 marks) (2) between RM2400 and RM2600? (3 marks) (3) at most RM2000? (3 marks)a) The following frequency distribution shows the investment capital (in RM'900) of a sample of 120 companies in the city: Investment capital (RM'000) Number of companies 200 to less than 300 7 300 to less than 400 18 400 to less than 500 23 500 to less than 600 37 600 to less than 800 21 800 to less than 1000 14 (i) Construct a "less than" cumulative frequency distribution for the above data and draw a "less than" ogive. (5 marks) (ii) From the ogive, estimate the (1) median and interpret the answer; (2 marks) (2) percentage of companies with investment capital more than RM650000. (2 marks) (iii) Calculate the mean and the standard deviation. (8 marks) Dr Steven has been teaching Economics for many years. He knows that 85% of the students will complete their assignments. Among those who complete their assignments, 90% will pass the course. Among those who do not complete their assignments, only $5% will pass the course. (i) Draw a well-labelled probability tree diagram with the joint probabilities calculated to illustrate the situation. (5 marks) (ii) Given that Stella took Economics last semester from Dr Steven and passed the course, what is the probability that she completed the assignments? (3 marks)Question 2 a) (Continued) (ii) If 10% of the fresh graduates have starting salaries of less than RM k, determine the value of k. (3 marks) b) Hin Seng Furniture would like to review the relationship between the amount spent on advertising and the sales revenue. The information on advertising expenses and sales for the last eight months was collected, and shown in the following table: Advertising Expense, X (RM '00,000) 3 6.5 5 4.5 2 8 6 3 Sales, Y (RM million) 4 9.6 6.2 6.5 3.8 10 9 4.4 X =38. [Y=53.5, >XY = 289.45. >X2 = 209.5, > Y2 = 403.65 (i) Calculate the product moment correlation coefficient between the advertising expenses and sales. Interpret your result. (5 marks) Calculate the coefficient of determination and interpret your answer. (2 marks) (iii) Rank the data and calculate the Spearman's rank correlation coefficient