Answer :
Answer:
9.48% probability that exactly 12 parts are produced in one day
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The number of defective parts produced by a process in one day has a Poisson distribution with a mean of 10.
This means that [tex]\mu = 10[/tex]
What is the probability that exactly 12 parts are produced in one day
This is P(X = 12).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 12) = \frac{e^{-10}*(10)^{12}}{(12)!} = 0.0948[/tex]
9.48% probability that exactly 12 parts are produced in one day