Answer:
The probability that exactly 15 defective components are produced in a particular day is 0.0516
Step-by-step explanation:
Probability function : [tex]P(X=x)=e^{-\lambda} \frac{\lambda^x}{x!}[/tex]
We are given that The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of 20.
So,[tex]\lambda = 20[/tex]
we are supposed to find the probability that exactly 15 defective components are produced in a particular day
So,x = 15
Substitute the values in the formula :
[tex]P(X=15)=e^{-20} \frac{20^{15}}{15!}[/tex]
[tex]P(X=15)=e^{-20} \frac{20^{15}}{15!}[/tex]
[tex]P(X=15)=0.0516[/tex]
Hence the probability that exactly 15 defective components are produced in a particular day is 0.0516
