Sonny's Super Market has installed a self-service checkout counter, and wishes to understand how this has affected customer service. Shoppers arrive on average the rate of one every other minute (Poisson distribution). Each shopper takes an average of 84 seconds to use the checkout, and that time is exponentially distributed. a. Calculate how long it takes, on average, for a shopper at the self-service counter, including how long they wait in line and how long it takes them to do their own checkout.'

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Business

Clay Pennington

21 September, 17:23

Sonny's Super Market has installed a self-service checkout counter, and wishes to understand how this has affected customer service. Shoppers arrive on average the rate of one every other minute (Poisson distribution). Each shopper takes an average of 84 seconds to use the checkout, and that time is exponentially distributed. a. Calculate how long it takes, on average, for a shopper at the self-service counter, including how long they wait in line and how long it takes them to do their own checkout.'

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Siena Kramer · Answer 1

The Expected time a customer spends in the system is 4

Explanation:

According to the given data we have the following:

Arrival rate A = 1 every other minute = 30/hour or (30/60) per minute

Service rate S = 84 seconds = 60*60/84 = 42.86 customers per hour

System utilization factor P = A/S = 30/42.86 = 0.699

Length of the system L = P / (1-P) = 0.699 / (1-0.699) = 2.322

Therefore, Expected time a customer spends in the system = L/A = 2.322 / (30/60) = 4.644=4