Trader Joe\'s has one register open with the customer service employee able to p

Question

Trader Joe's has one register open with the customer service employee able to process one customer every 6.3 minutes. There are approximately 3 customers checking out per hour (i.e., arrival rate during off-peak hour) What is the probability that there will be more than one customer waiting in line? Answer: Trader Joe's has one register open with the customer service employee able to process one customer every 6.3 minutes. There are approximately 3 customers checking out per hour (i.e., arrival rate during off-peak hour). What is the probability that there will be less than 3 customers waiting in line? Answer:

Explanation / Answer

Arrival rate (A) = 3 per hour

Service rate (S) = 6.3 minutes or 60/6.3 = 9.52 per hour

Probability of zero units in system (P0) = 1 - A/S = 1 - 3/9.52 = 0.69

Probability of 1 unit (P1) = P0*(A/S) = 0.69*(3/9.52) = 0.22

1) Probability of more than 1 unit = 1 - P0 - P1 = 1 - 0.69 - 0.22 = 0.09

Probability of 2 units (P2) = P0*(A/S)^2 = 0.69*(3/9.52)^2 = 0.07

2) Probability of less than 3 units = P0 + P1 + P2 = 0.69 + 0.22 + 0.07 = 0.98

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