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:
[tex]\boxed{P(X=k)=\frac{\lambda^k\cdot e^{-\lambda}}{k!}}[/tex]
We calculate the probability that a board 3 meters in length has no flaws. We get that k=3.
We calculate:
[tex]P(X=3)=\frac{0.45^3\cdot e^{-0.45}}{3!}\\\\P(X=3)=0.0097\\[/tex]
So, the probability is P=0.0097.
