A single inventory is controlled by a continuous review $($R$,$Q$)$ policy.

The lead time demand is normally distributed with mean $20$ and standard deviation $5.$

The average inventory position is $30$

The service level S$\_1=0\mathrm{.}90.$

a$)$ Calculate S$\_2.$

b$)$ Now instead the lead time demand follows an exponential distribution with mean $20$ Calculate S$\_1$

c$)$ Assume again that the lead time demand follows an exponential distribution with mean $20.$

Determine the value of R if we want to attain the same level of S$\_1$ as in the original case $(90\%)?$