Question

The Brampton store has customers arrive every 95 seconds and average service rate of 55 customers per hour. What is the average number of customers waiting in line? Answer to 2 decimal places.The Hamilton store has an arrival rate of 30. If the store wanted the average time in the system to be 6 minutes, what would the service rate have to be? Answer to one decimal place.The Brantford store has a service rate of 60 customers per hour. What is the probability that checkout time will take between 1 and 3 minutes.

Answer 1

The Brampton store has customers arrive every 95 seconds and average service rate of 55 customers per hour. What is the average number of customers waiting in line?

Given:

Arrival time = 95 seconds

Arrival rate λ= 1/95 = 0.0105263 customers per second = 0.0105263*3600= 37.8947 customers per hour

Service rate µ = 55 customers per hour

Required:

Average number of customers waiting in line Lq

Answer: 1.53 customers (to 2 decimal places)

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The Hamilton store has an arrival rate of 30. If the store wanted the average time in the system to be 6 minutes, what would the service rate have to be? Answer to one decimal place.

Given:

Arrival rate λ = 30

Average time in system = 6 minutes

Required:

Service rate:

µ = 4/0.1 = 40.0 customers per hour

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The Brantford store has a service rate of 60 customers per hour. What is the probability that checkout time will take between 1 and 3 minutes?

Given:

Service rate = 60 customers per hour =

Required:

Probability of checkout time between 1 and 3 minutes

Probability (1 to 3 min) = (P≤3) – (P≤1)

Probability = 0.3181