Norris Medical Clinic is staffed by a single physician who, on average, requires $15$ minutes to

treat a patient. The distribution of this service time follows a truncated normal distribution with

a standard deviation of $4$ minutes and a minimum value of $5$ minutes. Patients arrive at the

clinic according to the following probability distribution:

$($a$)$ Simulate $100$ patient arrivals using spreadsheet. For each patient, show the time between

arrival, arrival time, service start time, service time, service end time, and waiting time.

$(20$ marks$)$

$($b$)$ Based on $1$ replication,

$($i$)$ What is the average waiting time per patient?

$($ii$)$ What percentage of patients need to wait for more than $15$ minutes before service starts?

$(6$ marks$)$

$($c$)$ Replicate the above simulation for $200$ times using Data Table.

$(7$ marks$)$

$($d$)$ Based on $200$ replications,

$($i$)$ What is the average waiting time per patient?

$($ii$)$ On average, what percentage of patients need to wait for more than $15$ minutes before

service starts?

$($iii$)$ Develop a relative frequency table for the average waiting time per patient. Use class

intervals with the upper limits $5$ minutes, $10$ minutes, $15$ minutes, $20$ minutes, $25$

minutes, $30$ minutes, and more than $30$ minutes.

$($iv$)$ Plot a chart for the relative frequency table in part $($iii$),$ label everything clearly.

$(17$ marks$)$ please do with steps and formula especially for the part c question detailed steps