Question

The number of pits in a corroded steel coupon follows a Poisson distribution with a mean of 6 pits per cm2. Let X represent the number of pits in a 1 cm2 area. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
Find P(X = 2).

Answer 1

Answer:

P(X=2)=0.0446

Step-by-step explanation:

If X follows a Poisson distribution, the probability p to have x pits in 1 cm2 is calculated as:

$p(x)=\frac{e^{-m}*m^x}{x!}$

Where m is the mean of pits per cm2, so, replacing m by 6 pits per cm2, we get that the probability is equal to:

$p(x)=\frac{e^{-6}*6^x}{x!}$

Now, the probability P(x=2) that there are 2 pits in a 1 cm2 is calculated as:

$p(x=2)=\frac{e^{-6}*6^2}{2!}\\p(x=2)=0.0446$