In a continuous review inventory system, the lead time for door knobs is $5$ weeks. The standard deviation of demand during the lead time is $85$ units. The desired cycle$-$service level is $99$ percent. The supplier of door knobs streamlined its operations and now quotes a $1-$week lead time. How much can safety stock be reduced without reducing the $99$ percent cycle$-$service level?

$18.$ In a two$-$bin inventory system, the demand for $3-$inch lag bolts during the $2-$week lead time is normally dis$$tributed$,$ with an average of $53$ units per week. The standard deviation of weekly demand is $5$ units.

a$.$ What is the probability of demand exceeding the reorder point when the normal level in the second bin is set at $130$ units?

b$.$ What is the probability of demand exceeding the $130$ units in the second bin if it takes $3$ weeks to receive a replenishment order?