Widget Wonders, Inc. specializes in offering cutting-edge and imaginative children's toys. Recognizing the significance of the pre-holiday season for launching new products, the company strategically selects an October market entry date for potential holiday gifts. Each year, Widget Wonders places one-time orders with manufacturers in June or July to ensure the timely availability of toys in stores. This season, Widget Wonders is thrilled to introduce a novel product named SoundSphere. Developed by a renowned company in South Korea, SoundSphere is a unique musical instrument for kids. When touched, it produces harmonious sounds resembling various instruments, fostering creativity and musical exploration. The challenge faced by Widget Wonders is determining the optimal order quantity for SoundSphere, considering the inherent volatility in the demand for children's toys. The management team proposes order quantities of 12,000,15,000,20,000, and 24,000 units, reflecting diverse opinions on market potential. Issues and Recommendations: 1. Demand Distribution: - Utilize the sales forecaster's prediction, expecting an average demand of 18,000 units with a standard deviation of 3,000 units. Illustrate the normal probability distribution, emphasizing the mean and standard deviation. 2. Stock-Out Probability: - Employ the normal distribution to compute the probability of stock-outs for each proposed order quantity (12,000,15,000,20,000,24,000). 3. Projected Profit: - Calculate the projected profit for the suggested order quantities under three scenarios: worst case (sales =12,000 units), most likely case (sales =18,000 units), and best case (sales =24,000 units). 4. Manager's Policy: - Evaluate the manager's proposed policy, aiming for a 70\% chance of meeting demand and a 30% chance of stock-outs. Determine the order quantity and project profits under the three sales scenarios. 5. Recommendation: - Provide your order quantity recommendation based on a balanced consideration of profit potential and risk factors. 6. Rationale: - Justify your recommendation, taking into account historical data, market trends, and the company's overall strategy. This comprehensive report will guide Widget Wonders in making an informed decision regarding the order quantity for SoundSphere, ensuring a successful and profitable holiday season