1. **Problem Statement:** Omar wants to forecast the number of Joseph Smith carvings to be sold in Month 7 using two methods: a 4-month moving average and a 4-month weighted moving average. 2. **Given Data:** Month: 1, 2, 3, 4, 5, 6 Sales: 40, 58, 45, 54, 48, 44 3. **4-Month Moving Average Formula:** $$\text{Forecast for Month } n = \frac{\text{Sales}_{n-1} + \text{Sales}_{n-2} + \text{Sales}_{n-3} + \text{Sales}_{n-4}}{4}$$ 4. **Calculate 4-Month Moving Average for Month 7:** Use sales from Months 3, 4, 5, and 6: $$\frac{45 + 54 + 48 + 44}{4} = \frac{191}{4} = 47.75$$ 5. **4-Month Weighted Moving Average Formula:** $$\text{Forecast for Month } n = w_1 \times \text{Sales}_{n-1} + w_2 \times \text{Sales}_{n-2} + w_3 \times \text{Sales}_{n-3} + w_4 \times \text{Sales}_{n-4}$$ where weights sum to 1. 6. **Given Weights:** - Last month (Month 6): 0.7 - Two months previous (Month 5): 0.1 - Three months previous (Month 4): 0.1 - Four months previous (Month 3): 0.1 7. **Calculate Weighted Moving Average for Month 7:** $$0.7 \times 44 + 0.1 \times 48 + 0.1 \times 54 + 0.1 \times 45 = 30.8 + 4.8 + 5.4 + 4.5 = 45.5$$ **Final Answers:** - 4-month moving average forecast for Month 7: **47.75** - 4-month weighted moving average forecast for Month 7: **45.50**