Ask Question
12 August, 12:01

2. A manufacturer produces light bulbs at a Poisson rate of 300 per hour. The probability that a light bulb is defective is 0.012. During production, the light bulbs are tested, one by one, and the defective ones are put in a special can that holds up to a maximum of 50 light bulbs. On average, how long does it take until the can is lled

+4
Answers (1)
  1. 12 August, 12:15
    0
    On average it will take 13 hrs 53 minutes before the van is filled

    Step-by-step explanation:

    The first thing we need to do here is to find find the number of defective light bulbs

    Using the poisson process, that would be;

    λ * p

    where λ is the poisson rate of production which is 300 per hour

    and p is the probability that the produced bulb is defective = 0.012

    So the number of defective bulbs produced within the hour = 0.012 * 300 = 3.6 light bulbs per hour

    Now, let X be the time until 50 light bulbs are produced. Then X is a random variable with the parameter (r, λ) = (50, 3.6)

    What we need to find however is E (X)

    Thus, the expected value of a gamma random variable X with the parameter (x, λ) is;

    E (X) = r/λ = 50/3.6 = 13.89

    Thus the amount of time it will take before the Can will be filled is 13 hrs 53 minutes
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “2. A manufacturer produces light bulbs at a Poisson rate of 300 per hour. The probability that a light bulb is defective is 0.012. During ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers