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

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)=(e^(-\lambda)\lambda^x)/(x!)`

For x= 15 and
`\lambda=20` , we have

`P(X=x)=(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