$)$ Consider a workstation with a single machine. The processing times at the workstation are normally distributed with a mean of $4$ minutes and a standard deviation of $1\mathrm{.}2$ minutes. The workstation is stable and the machine utilization is $90\%.$ a$)$ What is the production rate of this workstation? b$)$ If inter$-$arrival times of jobs to this workstation is exponentially distributed, what is the average cycle time at this workstation? c$)$ What is the average cycle time if jobs are released to this workstation from a neighboring storage area in a deterministic fashion at the production rate calculated in part a$).$ d$)$ If the machine at this workstation starts experiencing outages where the time between two consecutive failures is exponentially distributed with rate $1$ failure per hour, what is the maximum mean$-$time$-$to$-$repair $($MTTR$)$ that will still ensure a stable operation for this workstation?