Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of $21$ gallons per week and a standard deviation of $3\mathrm{.}2$ gallons per week. The new manager desires a service level of $90$ percent. Lead time is two days, and the dairy is open seven days a week. $($Hint: Work in terms of weeks.$)$

Use Z tables. A$)$ If a fixed$-$interval model is used instead of an ROP model, what order size would be needed for the $90$ percent service level, with an order interval of $10$ days and a supply of $8$ gallons on hand at the order time? $($Do not round intermediate calculations. Round your final answer to the nearest whole number.$)$ B$)$ What is the probability of experiencing a stockout before this order arrives? $($Do not round intermediate calculations. Round your final answer to the nearest whole percent.$)$ C$)$ Suppose the manager is using the ROP model described in part a$.$ One day after placing an order with the supplier, the manager receives a call from the supplier that the order will be delayed because of problems at the supplier$$s plant. The supplier promises to have the order there in two days. After hanging up$,$ the manager checks the supply of walnut fudge ice cream and finds that $2$ gallons have been sold since the order was placed. Assuming the supplier$$s promise is valid, what is the probability that the dairy will run out of this flavor before the shipment arrives?