After analyzing the costs of various options for ob$-$ taining brackets, Ross White $($see Problems $6-27$ through $6-29)$ recognizes that although he knows that the lead time is $2$ days and the demand per day averages $10$ units, the demand during the lead time often varies. Ross has kept very careful records and has determined that lead time demand is normally distributed with a standard deviation of $1\mathrm{.}5$ units.

$($a$)$ What Z value would be appropriate for a $98\%$ service level?

$($b$)$ What safety stock should Ross maintain if he wants a $98\%$ service level?

$($c$)$ What is the adjusted ROP for the brackets?

$($d$)$ What is the annual holding cost for the safety stock if the annual holding cost per unit is $$1\mathrm{.}50?$