Weekly demand for a $3-$D printer retailer has a mean of $50$ units. The supplier has a lead time of $21$ days. Th placing an order to the supplier each time is $$8,$ and annual holding cost for one unit is $20$ percent of the Co Each unit costs the retailer $$208.$ Assume $52$ weeks in a year.

Assume there is a weekly standard deviation in demand of $10$ units $($Chapter $11).$

If we have on average $45$ units of on$-$hand inventory, what is our stock$-$out probability?

"The on$-$hand inventory in this question is independent from other questions

TABLE $11\mathrm{.}5$ In$-$Stock Probabilities and Matching Safety Factors, $z$

$\backslash$table$[[$In$-$Stock Probability,Safety Factor, $Z,$Safety Factor, $Z,$In$-$Stock Probability$],[0\mathrm{.}9000,1\mathrm{.}28,1\mathrm{.}25,0\mathrm{.}8944],[0\mathrm{.}9800,2\mathrm{.}05,2\mathrm{.}00,0\mathrm{.}9773],[0\mathrm{.}9900,2\mathrm{.}33,2\mathrm{.}25,0\mathrm{.}9878],[0\mathrm{.}9950,2\mathrm{.}58,2\mathrm{.}50,0\mathrm{.}9938],[0\mathrm{.}9999,3\mathrm{.}72,3\mathrm{.}00,0\mathrm{.}9987]]$

$2\mathrm{.}27\%$

$0\mathrm{.}62\%$

$2\mathrm{.}00\%$

$1\mathrm{.}22\%$

Question $2$