A carpenter makes bespoke rocking chairs. Each week, the number of chairs that he makes matches the demand received from a furniture shop. The probability that the shop demands 10 chairs is 0.4, the probability they demand 15 chairs is 0.35 and the probability they demand 20 chairs is 0.25. Each week he works with a different type of wood, which impacts how much it costs him to make the chairs. The probability the wood per chair costs 20 is 0.3 and the probability the wood per chair costs 30 is 0.7. The furniture shop pays the carpenter an amount dependent on the quality of his work. He makes 30 per chair with probability 0.15, 40 per chair with probability 0.60 or 45 per chair with probability 0.25. 5a. Using the top hat method, provide details of how you would simulate the variability in this situation. [5 marks] For each week the carpenter's profit can be calculated using the equation Profit = Demand* (Price - Materials). Use the following rows of the random number table to generate random variables: Demand: Row 1, i.e. 18 69 84 78 85 78 40... Materials: Row 2, i.e. 90 42 07 45 05 09 10... Price: Row 3, i.e. 11 39 93 93 42 79 66... Using two digit random numbers for all distributions, simulate 5 weeks of trade for the carpenter. 5b. What was the average profit the carpenter gained over the 5 weeks you simulated? Show all of your working. [6 marks] A) 270 B) 220 C) -50 D) 180 5c. What was the probability that the carpenter gained more than 200 in profit? [3 marks] A) 0 B) 0.5 C) 0.6 D) 0.8