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7 November, 09:47

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

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  1. 7 November, 13:27
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    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
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