Random Processes | Poisson or not? | Probability of doing n jobs in t hours

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SUMMARY

The discussion centers on calculating the probability of processing at least 50 jobs within 240 hours, given that the processing time for each job is a random variable with a mean and standard deviation of 2 hours. Participants suggest using the Central Limit Theorem (CLT) to approximate the distribution of the total processing time, as the processing times are independent. The application of the Poisson process is also considered, but the justification for its use requires clarification regarding the nature of the random variables involved.

PREREQUISITES
  • Understanding of Central Limit Theorem (CLT)
  • Knowledge of Poisson processes
  • Familiarity with Gaussian distribution
  • Basic probability concepts related to random variables
NEXT STEPS
  • Study the application of the Central Limit Theorem in probability distributions
  • Learn about Poisson processes and their conditions for use
  • Explore Gaussian distribution properties and calculations
  • Investigate methods for calculating probabilities of sums of random variables
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Students in statistics or probability courses, data analysts, and anyone involved in operations research or job scheduling optimization will benefit from this discussion.

dharavsolanki
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Homework Statement


The number of hours that it takes to process a certain type of job is a random variable with mean and standard deviation 2. AAssuming that processing times are independent, approximate the probability that atleast 50 jobs can be sequentially processed within 240 hours.


Homework Equations





The Attempt at a Solution


How should I approach this question? Can we use Poisson process for this equation? Please justify this point. Thank you again.
 
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Central Limit theorem looks appropriate using Gaussian distribution.
 
rootX said:
Central Limit theorem looks appropriate using Gaussian distribution.

Here are my doubts:

* Central Limit Theorem will apply on multiple random variables.What are the multiple random variables here? Processing time for each job?
* "atleast 50 jobs can be sequentially processed within 240 hours"... so the time required for each job in the sequence will be a random variable. How will i figure 240 hours here in the calculation?
 

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