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A vending machine dispenses hot chocolate or coffee. Service time is 40 seconds per cup and is constant. Customers arrive at a mean rate of 60 per hour, and this rate is Poisson-distributed.a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)Average number of customer _____ b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)Average time _____ minutesc. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Sagot :

tutorconsortium111

The average number of customers waiting is 1.33, with a time spent of 0.033 hours.

What is the rate of Poisson distribution?

Here given:

Arrival rate = 60 per hour

Service time = 40 seconds per cup

Service rate(µ) = 60/40

= 3/2per minute

= 3/2 x 60

= 90per hour

In response to the question:

It is a (M/M/1) Poisson distribution.

The following formula should be used:

a. The average number of customers in line.

Lq = λ²/ µ ( µ - λ)

b. Average amount of time that the customers spend in the system.

W = 1 / µ - λ

So , the average number of customers who are waiting.

Lq = λ²/ µ ( µ - λ)

60 x 60 / 90(90 - 60)

= 3600 / 90 x 30

= 3600 / 2700

Lq = 1.33

Average amount of time spent.

W = 1 / µ - λ

= 1 / 90 - 60

= 1 / 30

W = 0.033hr

As a result, the average number of customers waiting is 1.33, and the average time spent is 0.033hours.

To learn more about Poisson distribution refer to :

https://brainly.com/question/29378904

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