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# The number of flaws in a certain type of lumber follows a ISBN: 9780073401331 38

## Solution for problem 15E Chapter 4.3

Statistics for Engineers and Scientists | 4th Edition

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Problem 15E

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-by-Step Solution:

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 X poisson(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 X poisson(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

Step 3 of 3

##### ISBN: 9780073401331

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