Need help with Queuing Question!!!!!!

Offered Price: $ 10.00 Posted By: tomnorth3 Updated on: 06/28/2019 03:27 PM Due on: 06/28/2019
Question # 00728883 Subject Statistics Topic Data Analysis Tutorials:
Question
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A n immigration agent at Ataturk airport in istanbul, Turkey on the average could process 120 entrants during an 8 hour shift, if she was busy all of the time.  The number of arrivals is based on a Poisson distribution and the time to process each entrant is a random variable with an exponential distribution.  On the average, an entrant arrives at herstation once every 6 minutes.  Determine the probability that more than 3 people will be in line.

A) 80%

B) 20%

C) 10%

D) 3%

 

I think the answer is D - 3% but I do not know how to calculate it.  Lambda = 60/6 =10 and Mu=120/8=15.  The average number of people in line Lq = 100/15(15-10)=1.33.  The probability of 3 people being in line I calculate as =9.7%.  If the average is 1.33 and the question is more than 3 people, I would think the probability would be small and therefore 3% since it's the only answer less that 9%.

 

Thoughts????  Thanks!!!

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