Weekly demand for a $3-$D printer retailer has a mean of $50$ units. The supplier has a lead time of $21$ days. T 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 Probabllities and Matching Safety Factors, z

In$-$Stock Probabllity Safety Factor, Z

Safety Factor, z In$-$Stock Probablity

$0\mathrm{.}9000$

$1\mathrm{.}28$

$1\mathrm{.}25$

$0\mathrm{.}8944$

$0\mathrm{.}9800$

$2\mathrm{.}05$

$2\mathrm{.}00$

$0\mathrm{.}9773$

$0\mathrm{.}9900$

$2\mathrm{.}33$

$2\mathrm{.}25$

$0\mathrm{.}9878$

$0\mathrm{.}9950$

$2\mathrm{.}58$

$2\mathrm{.}50$

$0\mathrm{.}9938$

$0\mathrm{.}9999$

$3\mathrm{.}72$

$3\mathrm{.}00$

$0\mathrm{.}9987$

$2\mathrm{.}27\%$

$0\mathrm{.}62\%$

$2\mathrm{.}00\%$

O $1\mathrm{.}22\%$