QUESTION FOUR (a) A firm must decide which of two products to produce. Resources are only available for one of the products. The set up cost for product X are GHC50,000 and for product Y are GH 70,000 Other expenses (such as staff and material cost) are the same for both products. A market research study has been conducted to predict the probabilities of "high" and "low" expected gross profits (excluding set-up cost) for the two products. The results are shown below Expected Gross Profit Product X Product Y High 0.7 0.8 (GHC250,000) Low 0.3 0.2 (GHC100,000) 0 Construct a decision tree for this problem and determine which product will maximize the firms expected profit. Suppose that the "high" profit estimate is increased to GH350,000 which the probability remaining unchanged. Now find which product will maximize the firms expected profit [8 marks] (b) The distribution of the total loan amount defaulted by customers of a bank annually is approximated by a normal distribution. An average default amount is GHC 1.50 million and the standard deviation is GHc. 0.50 million. Required: Determine the probability that the total loan amount defaulted exceeds GHc. 1.50 million. Interpret your answer. ii. Determine the probability that the total amount defaulted is between GHC. 0.86 million and GHC. 0.90 million. Interpret your answer. ili. Determine the probability that the total amount defaulted is at most GHc. 2 million. Interpret your answer [9 marks QUESTION FOUR (a) A firm must decide which of two products to produce. Resources are only available for one of the products. The set up cost for product X are GHC50,000 and for product Y are GH 70,000 Other expenses (such as staff and material cost) are the same for both products. A market research study has been conducted to predict the probabilities of "high" and "low" expected gross profits (excluding set-up cost) for the two products. The results are shown below Expected Gross Profit Product X Product Y High 0.7 0.8 (GHC250,000) Low 0.3 0.2 (GHC100,000) 0 Construct a decision tree for this problem and determine which product will maximize the firms expected profit. Suppose that the "high" profit estimate is increased to GH350,000 which the probability remaining unchanged. Now find which product will maximize the firms expected profit [8 marks] (b) The distribution of the total loan amount defaulted by customers of a bank annually is approximated by a normal distribution. An average default amount is GHC 1.50 million and the standard deviation is GHc. 0.50 million. Required: Determine the probability that the total loan amount defaulted exceeds GHc. 1.50 million. Interpret your answer. ii. Determine the probability that the total amount defaulted is between GHC. 0.86 million and GHC. 0.90 million. Interpret your answer. ili. Determine the probability that the total amount defaulted is at most GHc. 2 million. Interpret your answer [9 marks