Stats-crv-exponential distribution

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SUMMARY

The discussion focuses on calculating probabilities related to the lifespan of light bulbs with a mean time to failure of 5000 hours. The first calculation determines that the probability of a randomly chosen light bulb still functioning after 10,000 hours is 0.1353, derived using the exponential distribution formula e^(-t/λ). The second part of the problem involves finding the probability that at least one out of five light bulbs remains operational after 10,000 hours, which requires using the complementary probability approach.

PREREQUISITES
  • Understanding of exponential distribution and its properties
  • Familiarity with probability calculations and complementary events
  • Knowledge of mean time to failure (MTTF) concepts
  • Basic mathematical skills for solving exponential equations
NEXT STEPS
  • Study the properties of the exponential distribution in depth
  • Learn how to apply the complementary probability method in various scenarios
  • Explore real-world applications of mean time to failure in reliability engineering
  • Practice solving similar probability problems involving multiple independent events
USEFUL FOR

This discussion is beneficial for students in statistics, reliability engineers, and anyone interested in understanding the lifespan and reliability of products using probability theory.

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Homework Statement



The time to failure for a certain light bulb in constant failure rate mode has a mean time to failure of 5000 hours.

What is the probability that a randomly chosen light bulb is still burning after 10,000 hours? Give answer to 4 decimals.

If 5 light bulbs are installed in different street lamps along Main Street, what is the probability that at least 1 will be working after 10,000 hours? Give answer to 4 decimals.


The Attempt at a Solution


I believe the first part would simply be e-(1/5000*10000)=.1353

The second part I am at a loss on how to solve it.
 
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