Calculating Probability for Vehicle Traffic at a Dual Carriageway Junction

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SUMMARY

The discussion focuses on calculating probabilities related to vehicle traffic at a dual carriageway junction, modeled by a Poisson distribution with a mean of 1.6 vehicles per minute. Participants are tasked with determining the probability of no vehicles passing in one minute, more than six vehicles passing in one minute, and fewer than three vehicles passing in five minutes. The Poisson probability density function is essential for these calculations, as it provides the necessary framework for determining these probabilities accurately.

PREREQUISITES
  • Understanding of Poisson distribution and its properties
  • Familiarity with probability density functions
  • Basic statistical calculation skills
  • Knowledge of mean and variance in probability theory
NEXT STEPS
  • Learn how to calculate probabilities using the Poisson distribution formula
  • Explore the application of Poisson distribution in real-world scenarios
  • Study the differences between Poisson and other probability distributions
  • Investigate statistical software tools for performing probability calculations
USEFUL FOR

Statisticians, data analysts, and anyone involved in traffic management or modeling vehicle flow at junctions will benefit from this discussion.

amcsquared
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Can someone help me out with this? (its not for school)

During the night the number of vehicles passing a particular junction on a dual carriageway follows a Poisson distribution with a mean of 1.6 vehicles per minute. Calculate the probability:
(i) That in a one minute period no vehicles pass the junction. (1)
(ii) That in a one minute period more than 6 vehicles pass the junction. (2)
(iii) That in a five minute period fewer than 3 vehicles pass the junction. (3)
 
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Well, do you know what the probability density function for a Poisson distribution looks like? Do you know what the values of that function represent?
 
Even if this question really is not for school, it still belongs in a homework forum. (I moved it)
 

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