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20cschultz
20cschultz
03.04.2021 • 
Mathematics

The manager has studied the truck arrival patterns and has determined that throughout the day, trucks randomly arrive at 23 per hour on average. Each scale station can scale 8 trucks per hour (7.5 minutes each). If the manager knew how many trucks would arrive during the hour, she would know how many scale stations to have open. For example, 0-8 trucks, open 1 scale station; 9-16 trucks, open 2 scale stations, etc. However, the number of trucks is a random variable and is uncertain. Your task is to provide guidance for the decision.

a. Based on the mean rate of 11 trucks per hour, what probability distribution should be used?
b. Use the probabilities fromthe first probability distribution above to create a probability distribution for the number of scale stations to open. For example, 0-4 trucks, open 1 scale station; 5-8 trucks, open 2 scale stations, etc. What is the expected number of scale stations needed?
c. Are there additional factors that should be considered? What are your recommendations for handling those factors?

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