I need help in this question. Please do it correctly and dont make it wrong. Please do it on MS WORD and copy/paste here and use the below formulas to do it.

Question 1 (50 points) A new dental clinic at which only one dentist works is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that patients will arrive at the desk at a rate of 24 per hour. It takes an average of 1.2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. a) What is the probability that the clinic is empty (except for the dentist)? (10 points) b) What is the probability that there are exactly five patients in the system? (15 points) c) Find the expected time a patient spends just waiting in line to have a question answered (time in the queue). (10 points) d) The cost of waiting time, in terms of patient unhappiness with the dental clinic, is $16 per hour of time spent waiting in line. Find the expected waiting costs over an 8-hour day. (15 points) Single Server, Exponential Service Time M/M/1 1. The average number of customers or units in the system, Ls Ls - 2. The average time a customer spends in the system, ws Ws 1 - Single Server, Exponential Service Time M/M/1 3. The average number of customers wating in the queue, La 22 (-) La = 4. The average time a customer spends waiting in the queue, W, wa (-) Single Server, Exponential Service Time M/M/1 5. System Utilization 2 p 6. Probability of O units in the system (that is, the service unit is idle) Po=1- u 7. Probability of more than k units in the system, where n is the number of units in the system k+1 Pn>k >k Single Server, Exponential Service Time M/M/1 2 = 2 cars arriving/hour u = 3 cars serviced/hour 2 Wa 2 (-) hour = 40 minutes average waiting time 3(3-2) = 2 = 66.6% of time mechanic is busy Po = 1 - 0.33 Probability there 0 cars in the system u