The Fore and Aft Marina is located on the Ohio River near Madison, Indiana. Fore and Aft currently operates a docking facility where only one boat at a time can stop for gas and servicing. and that the service rate for each server is $10$ boats per hour. $($Round your answers to four decimal places.$)$

$($a$)$ What is the probability that the boat dock will be idle?

$0\mathrm{.}2315$

$($b$)$ What is the average number of boats that will be waiting for service?

$0\mathrm{.}0593$

$($c$)$ What is the average time $($in hours$)$ a boat will spend waiting for service?

$($d$)$ What is the average time $($in hours$)$ a boat will spend at the dock?

$0\mathrm{.}0833q,$

$($e$)$ If customers expect to be able to be in and out of the marina within $10$ minutes on average, does this system provide acceptable service?

$,$ since the average time a boat will spend at the dock is

$10$ minutes. close to $10$ minutes as possible, but not exceeding $10$ minutes. Is enlarging the capacity of the dock to handle two boats at a time a good way of achieving this?

Both channels will be empty approximately

$\%$ of the time, and when customers do show up$,$ they

likely to have to wait for $10$ minutes. On the whole, the expansion

be best way of achieving their goal.