A manufacturing company doesn't charge its customers for shipping. It's products are small and lightweight, so there isn't much difference between the cost to ship small orders and large orders. Shipment costs average $84 per.
The company has a challenge to reduce its costs. One idea they are considering is charging customers for small orders. They did a survey asking customers what they would do if the company imposed a $90 fee on orders <$500. Of the 172 customers surveyed, 51 indicated they would pay the fee. The others said they would consolidate their orders.
The company estimated that customers who want to avoid the fee consolidate to realize a 33% reduction in their orders and a $1.15 million reduction in freight expense. The company's warehouse is run by a UConn MBA who aced OPIM 5110. She knows that it would be dangerous to bet her budget on such sketchy data. So, she decides to build a Monte Carlo model. She is responsible only for the freight budget, not incremental revenue. Using the data from the survey and the prior quarter's shipping volume, she assumed that the 45,800 orders would be candidates for consolidation and that the actual consolidation would be 33% with a standard deviation of 3.3%. She assumes normality in the distribution. She notes that shipping volumes are fairly steady over the past few quarters.
If her boss is asking for $1,250,000 in quarterly savings from the project, what % chance does this policy have of achieving it?