Question: A certain small grocery store has a single checkout stand with a full-time cashier. Customers arrive the stand according to a Poisson process at a

A certain small grocery store has a single checkout stand with a full-time cashier. Customers arrive the stand according to a Poisson process at a mean of 30 per hour. The time required to service customers has an exponential distribution with a mean of 15 per hour. Requirement:

Calculate the following

- What is the utilization rate of the grocery store?

- What is the average waiting time a customer spends in the queue of the store?

- What is the average number of customers in the store?

- What is the probability that a customer has to wait more than half an hour in the store?

- What is the probability that there are 5 customers in the store?

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