1. **Problem Statement:** Omar wants to forecast the number of Joseph Smith carvings to be sold in Month 7 using two methods: a 3-month moving average and a 3-month weighted moving average. 2. **3-Month Moving Average Formula:** $$\text{Forecast for Month } n = \frac{\text{Sales in } (n-1) + (n-2) + (n-3)}{3}$$ This method averages the sales of the last three months to predict the next month. 3. **Calculate 3-Month Moving Average for Month 7:** Sales for Months 4, 5, and 6 are 56, 55, and 41 respectively. $$\text{Forecast} = \frac{56 + 55 + 41}{3} = \frac{152}{3} = 50.67$$ 4. **3-Month Weighted Moving Average Formula:** $$\text{Forecast for Month } n = w_1 \times \text{Sales}_{n-1} + w_2 \times \text{Sales}_{n-2} + w_3 \times \text{Sales}_{n-3}$$ where weights $w_1=0.4$, $w_2=0.4$, and $w_3=0.2$. 5. **Calculate Weighted Moving Average for Month 7:** Using sales from Months 6, 5, and 4: $$\text{Forecast} = 0.4 \times 41 + 0.4 \times 55 + 0.2 \times 56 = 16.4 + 22 + 11.2 = 49.60$$ 6. **Final Answers:** - 3-month moving average forecast for Month 7: **50.67** - 3-month weighted moving average forecast for Month 7: **49.60**