Question

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

Answer 1

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