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.

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

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

For x= 15 and [tex]\lambda=20[/tex] , we have

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

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