$($Fictional$)$ Starbucks has decided to pilot an "early bird" opening at one of their busiest locations, opening at $4$:$30$ a$.$m$.$ to attract a population they cannot service with their standard opening time of $5$:$30a.m.$ They believe they can service the customers with a single cashier $/$ barista $($i$.$e$.$ one person$).$ The Store Operations group at headquarters has estimated that the single barista can service $60$ customers per hour. The local Starbucks marketing team has estimated that customers will arrive at this store at an average rate of one customer every $1\mathrm{.}2$ minutes $(50$ customers per hour$),$ even at this early time.

Answer the following for the time slot of $4$:$30$ a$.$m$.$ to $5$:$30$ a$.$m$.(2$pts each$)$

What can a store manager expect the average utilization rate to be$?$ Type your answer in $\%$ and round to $2$ decimal places

$(\%)$

In terms of the customer experience, how long should customers expect to spend getting their coffee, i$.$e$.$ inclusive of wait time and service time? Round your answer to $2$ decimal places

$($Minutes$)$

How much of that total time spent is time waiting? Round your answer to $2$ decimal places

$($Minutes$)$

What is the average number of customers waiting in line over the course of the hour? Round$-$up your answer to a whole number $($Customers$)$