At a walk-in clinic, patients arrive every 12 minutes on average (negative exponential distribution), and it takes about 8 minutes for the physician to diagnose the patient (negative exponential distribution). Please show your work in Excel with all formulas and calculations.

Part A: What are (average arrival rate) and (average service rate)?

Part B: On average, how long do patients wait to see the physician?

Part C: On average, how many patients are there at the clinic?

Part D: In an 8-hour day, how many hours is the physician idle?

Part E: What is the probability that there are more than 4 patients at the clinic?