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