The annual demand for a specific product is $3,500$ units and has the following ordering and holding costs:$$ Co $=$ $$20\mathrm{.}50$ per order and Ch $=$ $$8\mathrm{.}00$ per unit. Demand exhibits some variability such that the lead$-$time demand follows a normal probability distribution with $=45$ units and $=12$ units.$$What is the recommended order quantity for this product? If the manager sets the reorder point at $55$ units, what is the probability of a stockout in any given order cycle? Express your answer as a decimal to $4$ decimal places using standard rounding rules. Given the probability of a stockout in problem $2$b$,$ how many times would expect a stockout to occur during the year if the reorder point $=55$ units were used? Express your answer to $2$ decimal places using standard rounding rules. Using the information in Problem $2,$ assume that the company wants at most a $2\%$ probability of a stockout during any given order cycle.$$ Answer the following questions:

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Problem $2$d$.(2\mathrm{.}5$ points$)$ What is the Z$-$value if the company wants at most a $2\%$ probability of a stockout? Express your answer to $2$ decimal places using standard rounding rules.$$ What is the reorder point if the company wants at most a $2\%$ probability of a stockout? Express your answers as a whole number using standard rules.$$