4. A large toy company Mttel currently allows toy retailers to place orders with delivery in 3 weeks. The Gigantic Pocket Monster (Gipokmon) is a new toy that Mttel has introduced. TOYS-are-MINE plans to uses the order-up-to model (with a fill-rate target of 97%) to plan orders and deliveries to their retailers.

Given that this is a new toy, sales estimates are somewhat uncertain. The market research team is fairly confident that weekly demand would be normally distributed with a mean of 100 units. However, since this is a new product, demand uncertainty, as characterized by the standard deviation, is harder to estimate and could be either:

i. standard deviation of 30; or

ii. standard deviation of 25 units; or

iii. standard deviation of 20 units.

In order to budget working capital investment in inventories, you are required to provide an estimate of expected on-hand inventories for each level of uncertainty.Please show your work.