$4.$ In the process below, as shown, $240$ patients visit a clinic each day. After registration at step $1,$ usually each patient has to wait for $5$ mins in average, before they$$ll get assessed for the right next step based on their documentation in hand. Once step $2$ is complete, usually $40\%$ of the patients go to step $3,$ which takes $15$ minutes in average, and the rest are directed to step $4.$

$4-1)$ What is the hourly rate of patients$$ arrival in this clinic? $(4$ points$)$

$4-2)$ Calculate the value of T$1,$ I$2,$ I$3,$ and T$4(4$ points$)$

$4-3)$ What is the total process flow time based on your calculations above? $(4$ points$)$

$4-4)$ What is the total inventory of patients at this clinic at any given point in time? $(4$ points$)$