Final answer:
To find the probability of exactly five flaws in a 140-yard piece of material, we can use the Poisson distribution. The probability is approximately 0.146.
Step-by-step explanation:
To find the probability of exactly five flaws in a 140-yard piece of material, we can use the Poisson distribution. The Poisson distribution is used when the average number of events occurring in a fixed interval of time or space is known. In this case, the average number of flaws per 140 yards is 6.
The formula for the Poisson distribution is:
P(X=k) = (e^-λ * λ^k) / k!
Where P(X=k) is the probability of exactly k flaws, λ is the average rate of occurrence, and k is the number of flaws we want to find the probability for.
Plugging in the values, we have:
P(X=5) = (e^-6 * 6^5) / 5!
Calculating this, we find that the probability of exactly five flaws in a 140-yard piece of material is approximately 0.146.