Solving Poisson Distribution Homework for 50 Liters of Sediment

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SUMMARY

The discussion centers on calculating the probability of finding one or more prehistoric artifacts in a 50-liter sediment sample, given an artifact density of 1.0 per 10 liters. The relevant formula used is the Poisson probability mass function, P(r) = (e^-lambda)*(lambda^r)/r!. The correct value for lambda (λ) is determined to be 5, as it represents the average number of artifacts expected in 50 liters (1 artifact per 10 liters multiplied by 5). Participants clarify that to find the probability of one or more artifacts, one must calculate 1 - P(0), where P(0) is the probability of finding zero artifacts.

PREREQUISITES
  • Understanding of Poisson distribution
  • Familiarity with the Poisson probability mass function
  • Basic knowledge of exponential functions
  • Ability to perform calculations involving factorials
NEXT STEPS
  • Study the derivation and applications of the Poisson distribution in real-world scenarios
  • Learn how to calculate cumulative probabilities using the Poisson distribution
  • Explore advanced statistical concepts such as the Central Limit Theorem
  • Practice solving problems involving different distributions, including normal and binomial distributions
USEFUL FOR

Students in statistics or mathematics, archaeologists conducting quantitative analyses, and anyone interested in applying statistical methods to real-world problems involving artifact density and sampling.

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Homework Statement


In one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.0. Suppose you are going to dig up and examine 50 liters of sediment at this site. Let r = 0, 1, 2, 3,… be a random variable that represents the number of prehistoric artifacts found in your 50 liters of sediment. Find the probability that you will find 1 or more artifacts in the 50 liters of sediment. Round your answer to the nearest ten thousandth.


Homework Equations


P(r) = (e^-lambda)*(lambda^r)/r!

The Attempt at a Solution


What is lambda? is it 10? or is it 10/50=0.2? i can't seem to figure it out.
i think r = 1
 
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λ is the number of artifacts in the 50 liters of sediment on average.

P(1) would be the probability you'd find exactly one artifact in the 50-liter sample, but the problem is asking you to find the probability of finding one or more. So you can't just set r=1 to get the answer you're looking for.
 

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