Hello. I need help with the following problem. Please show work!

Problem 10-12 L. Winston Martin (an allergist) has an excellent system for handling his regular patients who come in just for allergy injections. Patients arrive for an injection and fill out a name slip, which is then placed in an open slot that passes into another room staffed by one or two nurses. The specific injections for a patient are prepared, and the patient is called through a speaker system into the room to receive the injection. At certain times during the day, patient load drops and only one nurse is needed to administer the injections. Use Exhibit 10.9. Let's focus on the simpler case of the two-namely, when there is one nurse. Also, assume that patients arrive in a Poisson fashion and the service rate of the nurse is exponentially distributed. During this slower period, patients arrive with an interarrival time of approximately 4 minutes. It takes the nurse an average of 3.20 minutes to prepare the patients' serum and administer the injection. a. What is the average number of patients you would expect to see in Dr. Martin's facilities? (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places.) Answer is complete but not entirely correct. Average number of 1.33 X patients b. How long would it take for a patient to arrive, get an injection, and leave? (Round your answer to 2 decimal places.) Answer is complete but not entirely correct. Average total time 22.66 X minutes c. What is the probability that there will be three or more patients on the premises? (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.) Answer is complete but not entirely correct. Probability 0.6 % d. What is the utilization of the nurse? (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.) Answer is complete but not entirely correct. Utilization of the 0.9 X % nurse e. Assume three nurses are available. Each takes an average of 3.20 minutes to prepare the patients' serum and administer the injection. What is the average total time of a patient in the system? (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places. Do not interpolate your Nu ratio when using Exhibit 10.9. Use the closest Nu ratio appearing in the table.) Answer is complete but not entirely correct. Average total time 19.56 X minutes