QUESTION 1 Mark: 3+1+3 = 7 The checking-in time at a hotel is to be investigated. Historically, the process has had a standard deviation of 0.08. The means of 30 samples of 20 observations each given in minute in the table below: Sample 1 Sample 21 22 23 24 3 4 5 6 7 Mean 3.80 3.84 3.87 3.82 3.84 3.78 3.89 3.75 3.84 3.80 Sample 11 12 13 14 15 16 17 18 19 20 Mean 3.90 3.86 3.88 3.79 3.83 3.86 3.92 3.83 3.84 3.82 25 26 27 28 29 30 Mean 3.85 3.89 3.81 3.86 3.83 3.90 3.86 3.83 3.85 3.86 9 10 i. ii. Construct a mean control chart for this process of checking-in with three-sigma (z= 3) limits. Is the process in control? Analyze the data using the median run-test and the up/down run-test and provide your conclusion. QUESTION 2 Mark: 1+2+1+2+2 = 8 a) A university cafeteria is a self-service facility in which a customer selects the food items he/she wants and then following a single line pays the cashier. Customers arrive at a rate of about 5 per minute according to the Poisson distribution. The single cashier ringing up sales takes about 10 seconds per customer, following the negative exponential distribution. i. What is the utilization rate of serving the customer? ii. What is the probability of no customer in the system? jii. What is the average number of customers in the system? What is the average number of customers in the line? What is the probability that there are over 6 customers in the system? iv. V