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Andrew [12]
3 years ago
12

The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of 20. Each d

efective component has probability 0.60 of being repairable. Find the probability that exactly 15 defective components are produced in a particular day. Round your answer to four decimal places.
Mathematics
1 answer:
liberstina [14]3 years ago
7 0

Answer: 0.0516

Step-by-step explanation:

Given : The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of \lambda=20.

The probability mass function for Poisson distribution:-P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}

For x= 15 and  \lambda=20 , we have

P(X=x)=\dfrac{e^{-20}(20)^{15}}{15!}=0.0516488535318\approx0.0516

Hence, the probability that exactly 15 defective components are produced in a particular day = 0.0516

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So, total liking either one or neither = 4 + 5 + 5 + 6 = 20

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