Demand for a coffee cup is normally distributed with a mean of $18$ units per week and a standard deviation in weekly demand of $5$ units. The lead time is $2$ weeks, and the business operates $52$ weeks per year. The continuous review system called for an EOQ of $75$ units and a cycle$-$service level of $90$ percent $($for $90\%$ service level, assume the value of z $=1\mathrm{.}28).$ What is the target level under periodic review system $($P system$)?$

Group of answer choices

$127$ units

$147$ units

$157$ units

$137$ units

$117$ units