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Q5. During peak hours, customers arrive at the cashier check-out queue in a local supermarket according...

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Advance Math

Q5. During peak hours, customers arrive at the cashier check-outqueue in a local supermarket according to a Poisson process with anaverage rate of 120 customers per hour. There are four cashiersserving the check-out, and they provide identical service tocustomers. The time to service any customer by any of the cashieris exponentially distributed with a mean of 20 seconds. If all thecashiers are busy, customers join in a single queue on arrival.

(a) Compute the probability that an arriving customer have towait in the queue for an available cashier;
(b) Suppose the supermarket opens at 10am, and Peter arrives at thecashier check-out at 10.02am. What assumptions are needed toapproximate the probability that Peter do not have to queue.

Pls explain with workings. Thxs

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