A horologist $($watchmaker$)$ is typically able to scrvice a mechanical watch in about $120$ minutes $($exponential distribution$).$ Assuming an $8$ hour work$-$day, the watchmaker averages s customers arriving at his shop every day following a poisson distnbution. The watchmaker just purchased a new machinc that wil polish the dial and crystal reducing his service time bi $20$ minutes per watch. How much will the line for a watch waiting to be serviced be reduced by the watchmaker using this new machinc, assuming, no increase in customer demand?