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 2 every 15 minutes, what proportion of the time is the server busy (utilized)?

a. 0.25b. 0.50c. 0.75d. 2.25e. 3.00

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Answer:

Option c is right

Step-by-step explanation:

Given that 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.

service rate per customer = [tex]\frac{15}{2} =7.5[/tex]

Average number of arrivals per hour = 6

Service time for 6 customers = [tex]7.5*6=45[/tex] minutes

i.e. on an average per hour the server is buy in 45 minutes

Proportion = [tex]\frac{45}{60} =0.75[/tex]

Option c is right