Question

Consider a Poisson probability distribution in a process with an average of 3 flaws every 100 feet. Find the probability of 4 flaws in 100 feet.

Answer 1

Answer:

16.80% probability of 4 flaws in 100 feet.

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.

An average of 3 flaws every 100 feet.

So $\mu = 3$

Find the probability of 4 flaws in 100 feet.

This is $P(X = 4)$

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

$P(X = 4) = \frac{e^{-3}*(3)^{4}}{(4)!} = 0.1680$

16.80% probability of 4 flaws in 100 feet.