In a certain lumberyard, a survey of 3912 linear feet of pine 2-in.x12-in. dimension lumber found 517 large knots, defined as knots having a diameter of at least 1 inch. If the occurrence of knots follows a Poisson distribution, what is the probability that a particular 17-foot length of this lumber will contain more than 2 knots?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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In a certain lumberyard, a survey of 3912 linear feet of pine 2-in.x12-in. dimension lumber found 517 large knots,
defined as knots having a diameter of at least 1 inch. If the occurrence of knots follows a Poisson distribution, what is
the probability that a particular 17-foot length of this lumber will contain more than 2 knots?
Transcribed Image Text:In a certain lumberyard, a survey of 3912 linear feet of pine 2-in.x12-in. dimension lumber found 517 large knots, defined as knots having a diameter of at least 1 inch. If the occurrence of knots follows a Poisson distribution, what is the probability that a particular 17-foot length of this lumber will contain more than 2 knots?
Expert Solution
Step 1

Given information:-

3912 linear feet of pine found 517 large knots

The average number of knots in 17 foot length of this lumber=5173912×17=0.312157464×17=2.2466768922.2467

Determine the required probability using the poisson distribution:

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