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:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
[tex]e = 2.71828[/tex] is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
An average of 3 flaws every 100 feet.
So [tex]\mu = 3[/tex]
Find the probability of 4 flaws in 100 feet.
This is [tex]P(X = 4)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 4) = \frac{e^{-3}*(3)^{4}}{(4)!} = 0.1680[/tex]
16.80% probability of 4 flaws in 100 feet.
