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jasenka [17]
3 years ago
12

The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a m

ean of 0.025 failures per hour. (a) What is the probability that the instrument does not fail in an 8-hour shift
Mathematics
1 answer:
photoshop1234 [79]3 years ago
7 0

Answer: 0.1353

Step-by-step explanation:

Given : The mean of failures =  0.025 per hour.

Then  for 8 hours , the mean of failures = \lambda=8\times0.25=2 per eight hours.

Let X be the number of failures.

The formula to calculate the Poisson distribution is given by :_

P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}

Now, the probability that the instrument does not fail in an 8-hour shift :-

P(X=0)=\dfrac{e^{-2}2^0}{0!}=0.1353352\approx0.1353

Hence, the the probability that the instrument does not fail in an 8-hour shift = 0.1353

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