I need assitance with solving this Problem 3 PART D . I made numerous attempts to solve. however I am still having issues. Please provide a step by step explanation so, I can use it as notes for future reference. Respectfully thank you At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume there is only one lane and one inspector, who can inspect vehicles at the rate of 12 per hour in an exponentially distributed fashion.a. What is the average length of the waiting line? (Round your answer to 2 decimal places.)- **Answer is complete and correct.**- Average length: \(4.17\) customersb. What is the average time that a vehicle must wait to get through the system?- **Answer is complete and correct.**- Average time: \(30\) minutes **Question:**d. What is the probability that when you arrive there will be three or more vehicles ahead of you? *(Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.)***Response Box:**- Probability: 46.2 %**Feedback:**- "Answer is complete but not entirely correct."**Explanation:**The question asks for the probability of encountering three or more vehicles ahead upon arrival. The answer provided is 46.2%, but the feedback indicates there may be a small error or rounding issue in the calculations. It is important to ensure both intermediate and final rounding adhere to the specified number of decimal places for accuracy.

Given data: Arrival rate (λ) = 10 / hr Service rate (μ) = 12/ hrSolution: *As mentioned part (d) Probability of 0 vehicles in the system = P0 = 1 - λμ = 1 - 1012 = 1 - 0.833 = 0.167 Probability of 1 vehicle in the system = P1 = 1-λμ × λμ= 0.167× 0.833 = 0.139 Probability of 2 vehicles in the system = P2 = 1 - λμ× λμ × λμ= 0.167 x 0.833 x 0.833 = 0.116 Thus, Probability fo 3 or more vehicles in the system = 1-(P0+P1+P2)=1 - (0.167 + 0.139+ 0.116)= 0.578 = 57.8% (Rounding off to 1 decimal place) Probability will be three or more vehicles ahead = 57.8 %

Business

Operations Management

d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.) Answer is complete but not entirely correct. Probability 48.2

d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.) Answer is complete but not entirely correct. Probability 48.2

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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