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A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 3 every 15 minutes:What is the average number of customers in the system?
A. 0.50B. 1.00C. 2.25D. 3.00E. None of the above

Respuesta :

Answer:  Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Average number of arrivals = 6 per hour

Service rate = 3 every 15 minutes

Service rate is given by

[tex]\mu=\dfrac{60\times 3}{15}=12[/tex]

So, the average number of customers in the system is given by

[tex]\dfrac{\mu}{\mu-\lambda}\\\\=\dfrac{6}{12-6}\\\\=\dfrac{6}{6}\\\\=1[/tex]

Hence, Option 'c' is correct.

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