Question

The number of flaws in a certain type of lumber follows a Poisson distribution with a rate of 0.45 per linear meter. What is the probability that a board 3 meters in length has no flaws

Answer 1

Answer:

So, the probability is P=0.0097.

Step-by-step explanation:

We know that the  number of flaws in a certain type of lumber follows a Poisson distribution with a rate of 0.45 per linear meter.  

We conclude that  λ=0.45.

We use the Poisson formula:

$\boxed{P(X=k)=\frac{\lambda^k\cdot e^{-\lambda}}{k!}}$

We calculate the  probability that a board 3 meters in length has no flaws. We get that k=3.

We calculate:

$P(X=3)=\frac{0.45^3\cdot e^{-0.45}}{3!}\\\\P(X=3)=0.0097$

So, the probability is P=0.0097.