Example $1)$ From $6$am to $9$am customers arrive in droves to Bettys Bakery for her annual $1-$day cake sale. During that $3-$hour period, $1\mathrm{.}75$ customers enter the bakery every minute. Betty and her staff can box cakes and check out customers at a rate of $72$ per hour. a$)$ How much time does it take to serve a customer who arrives at $8$am$?$b$)$ How many customers are in line at $8$:$20$am$?$c$)$ How much time does it take to serve the $70$th customer in line?d$)$ How long, on average, does it take to serve customers during the $1-$day sale? Example $2)$ A small veterinary clinic in Bedford currently has a single veterinarian on staff. During normal operating hours, patients arrive at the clinic about every $50$ minutes. However, patient interarrival times vary with a standard deviation of $25$ minutes. Appointments take an average of $45$ minutes to complete and vary with a standard deviation of $22\mathrm{.}5$ minutes. a$)$ How much time, on average, do patients wait before being seen by the veterinarian?b$)$ On average, how many patients are waiting for service?c$)$ What is the average flow time for a patient?