Problem $3)$ A plumbing supplies distributor has determined that demand for a purchased item averages $112$ units per week with a standard deviation of weekly demand equal to $22\mathrm{.}3$ units. The purchasing lead$-$time is $3$ weeks. Answer the following questions assuming the company is willing to accept a stockout risk of no more than $2\mathrm{.}2\%(\mathrm{.}0220).12$ points

Appendix B$,$ Table B from Textbook

$\backslash$table$[[$Z$,.00,.01,.02,.03,.04,.05,.06,.07,.08,.09],[1\mathrm{.}5.9332.9345.9357.9370\mathrm{.}9382\mathrm{.}9394\mathrm{.}94069418.9429.9441],[],[],[1\mathrm{.}8.9641.9649\mathrm{.}96569664\mathrm{.}96719678\mathrm{.}9686\mathrm{.}9693\mathrm{.}9699\mathrm{.}9706],[],[]]$

a$.$ What is the acceptable stockout risk?

What is the required service level?

What $z$ value should be used?

b$.$ How much safety stock should he held? Show your work using the Microsoft Word equation editor or by typing to the right of the equation without using the equation editor. Round your answer up to an integer value if you calculate a fractional value.

c$.$ What reorder point should be used? Show your work using the Microsoft Word equation editor or by typing to the right of the equation without using the equation editor. Round your answer up to an integer value if you calculate a fractional value.