Question

The number of defective parts produced by a process in one day has a Poisson distribution with a mean of 10. Each defective part has probability of 0.6 of being repaired. What is the probability that exactly 12 parts are produced in one day

Answer 1

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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ 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 $\mu = 10$

What is the probability that exactly 12 parts are produced in one day

This is P(X = 12).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 12) = \frac{e^{-10}*(10)^{12}}{(12)!} = 0.0948$

9.48% probability that exactly 12 parts are produced in one day