Hey, can you please help me with these questions? Thanks!

1) The local hospital's emergency department has 6 trauma bays. On average, patients requiring atrauma bay arrive every 30 minutes (with a coefficient of variation of 1). If the hospital has an available trauma bay, it is immediately allocated to a needy patient. If there are no trauma bays available, the patient has to wait in the waiting room ("buffer"). On average, a patient's length of stay in a trauma bay is 1.5 hours (with a standard deviation of 1.5 hours). The hospital's emergency department operates 24 hours a day (a) What are the arrival rate and (total) service rate in [patients/hr]? b) What is the utilization? (c) What is the average waiting time for the patients? (d) The hospital updated the operating procedures for its staff. This led to a reduction in the standard deviation of the length of stay in a trauma bay from 1.5 to 1.25 hour and a reduction in the mean from 1.5 to 1 hour. What is the new average waiting time after this change? 2) A chocolate factory has weighed 4 chocolate truffles coming out of production over 5 workingdays to obtain the following data, weights are in grams. Mon Tue Wed Thu Fri 10am 30.50 30.30 30.15 30.60 30.15 11am 29.75 31.00 29.50 32.00 30.25 2pm 29.90 30.20 29.75 31.00 30.50 3pm 30.25 30.50 30.00 30.00 29.70 a) Group the data by day into five samples and find the sample average and range for each of the five samples .b) Construct the control limits of the X-bar chart. Is there any out of control sample? c) Construct the control limits of the R-chart. Is there any out of control sample?