Automobiles arrive at the drive-through window at the downtown Baton Rouge, Loui

Question

Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at the rate of 4 every 10 minutes. The average service time is 1.0 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.

a) The average time a car is in the system= 1.67 minutes

b) The average number of cars in the system= ____ cars (round to two decimal places)

c) The average number of cars waiting to recieve service= _____ cars (Round to two decimal places)

d) The average time a car is in the queue=____minutes(Round to two decimal places)

e) The probability that there are no cars at the window=_____(Round to two decimal places)

f) The percentage of time the postal clerk is busy= ____% (Round to nearest whole number)

g) The probability that there are at least 2 cars in the system=____ (Round to three decimal places)

h) If a second drive-through window, with its own server, were added, the average time a car is in the system= ____minutes (round to two decimal places)

Explanation / Answer

a) The average time a car is in the system= 1.67 minutes

b) The average number of cars in the system= 0.67 cars (round to two decimal places)

c) The average number of cars waiting to recieve service= 0.27 cars (Round to two decimal places)

d) The average time a car is in the queue= 0.67 minutes(Round to two decimal places)

e) The probability that there are no cars at the window= 0.6 (Round to two decimal places)

f) The percentage of time the postal clerk is busy= 0.4 % (Round to nearest whole number)

g) The probability that there are at least 2 cars in the system= 0.1 (Round to three decimal places)

h) If a second drive-through window, with its own server, were added, the average time a car is in the system= 1.04 minutes (round to two decimal places)

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