Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of two jobs per $8-$hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of $2\mathrm{.}7$ hours and a standard deviation of $1\mathrm{.}9$ hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs.

$($a$)$ What is the mean arrival rate in jobs per hour? $($Round your answer to four decimal places.$)$

per hour

$($b$)$ What is the mean service rate in jobs per hour? $($Round your answer to four decimal places.$)$

per hour

$($c$)$ What is the average number of jobs waiting for service? $($Round your answer to four decimal places.$)$

$($d$)$ What is the average time $($in hours$)$ a job waits before the welder can begin working on it$?($Round your answer to two decimal places.$)$

$h$

$($e$)$ What is the average number of hours between when a job is received and when it is completed? $($Round your answer to two decimal places.$)$ h

$($f$)$ What percentage of the time is Gubser's welder busy? $($Round your answer to the nearest whole number.$)\%$