Problem $2(10$ points$)$ A local emergency department $($ED$)$ maintains six nurses staffed per shift. Patients arrive to the ED according to a Poisson distribution with a mean of six per hour and are first seen by a nurse. Time spent with ED nurses is exponentially distributed with a mean of $30$ minutes. Use the Excel queueing template to answer the following questions

a$)$ What is the average number of patients waiting to be seen by a nurse?

b$)$ What is the probability that none of the nurses are with a patient?

c$)$ What is the average time spent waiting to be seen by a nurse?

d$)$ What is the utilization rate of the nursing staff?