Question: 3. Problem 3 (10pt) Consider the check-out counter at a local grocery store. Customers arrive at the check-out counter every 10 min on average with

3. Problem 3 (10pt) Consider the check-out

3. Problem 3 (10pt) Consider the check-out counter at a local grocery store. Customers arrive at the check-out counter every 10 min on average with a standard deviation of 7 min. The store has only one cashier who scans and bags the groceries. It takes the cashier 9 min on average with a standard deviation of 5 min to scan and bag the groceries for a customer. a. What is the utilization of the cashier? (1pt) b. What is the average waiting time for a customer? (3pt) c. What is the average number of customers waiting in the check-out line (i.e., excluding any customer being served)? (1pt) d. After attending a training program, the cashier can scan and bag groceries for a customer in 6 min on average with a standard deviation of 3 min. What is the reduction in average customer waiting time in minutes) because of this training program? (5pt) 3. Problem 3 (10pt) Consider the check-out counter at a local grocery store. Customers arrive at the check-out counter every 10 min on average with a standard deviation of 7 min. The store has only one cashier who scans and bags the groceries. It takes the cashier 9 min on average with a standard deviation of 5 min to scan and bag the groceries for a customer. a. What is the utilization of the cashier? (1pt) b. What is the average waiting time for a customer? (3pt) c. What is the average number of customers waiting in the check-out line (i.e., excluding any customer being served)? (1pt) d. After attending a training program, the cashier can scan and bag groceries for a customer in 6 min on average with a standard deviation of 3 min. What is the reduction in average customer waiting time in minutes) because of this training program? (5pt)

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