The number of flaws in a certain type of lumber follows a Poisson distribution with a rate of 0.45 per linear meter.

a. What is the probability that a board 3 meters in length has no flaws?

b. How long must a board be so that the probability it has no flaw is 0.5?

Step 1 of 3</p>

Given the no.of flaws in a lumber follows a poisson distribution with mean 0.45 per meter

Let X is the no.of flaws

Here Xpoisson(0.45)

The pmf of poisson distribution is P(x)=; x=0,1,2,...........

Step 2 of 3</p>

a) we have to find the probability that in 3 meters length has no flaws

For one meter 0.45 flaws

For 3 meters 3(0.45)= 1.35 flaws

Hence Xpoisson(1.35)

Here =1.35

Now P(X=0)=

=0.2592

Hence the probability that in 3 meters length has no flaws is 0.2592