Answer:
99.97% probability of observing less than 5 errors in the carpet
Step-by-step explanation:
The only information that we have is a mean during an interval. So we use the Poisson distribution solve this question.
We have that the probability of exactly x events is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*(\mu)^{x}}{x!}[/tex]
In which [tex]\mu[/tex] is the mean.
The number of weaving errors in a twenty-foot by ten-foot roll of carpet has a mean of 0.6.
This means that [tex]\mu = 0.6[/tex]
What is the probability of observing less than 5 errors in the carpet?
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
[tex]P(X = x) = \frac{e^{-\mu}*(\mu)^{x}}{x!}[/tex]
[tex]P(X = 0) = \frac{e^{-0.6}*(0.6)^{0}}{0!} = 0.5488[/tex]
[tex]P(X = 1) = \frac{e^{-0.6}*(0.6)^{1}}{1!} = 0.3293[/tex]
[tex]P(X = 2) = \frac{e^{-0.6}*(0.6)^{2}}{2!} = 0.0988[/tex]
[tex]P(X = 3) = \frac{e^{-0.6}*(0.6)^{3}}{3!} = 0.0198[/tex]
[tex]P(X = 4) = \frac{e^{-0.6}*(0.6)^{4}}{4!} = 0.0030[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.5488 + 0.3293 + 0.0988 + 0.0198 + 0.0030 = 0.9997[/tex]
99.97% probability of observing less than 5 errors in the carpet
Answer:
99.97% probability of observing less than 5 errors in the carpet
Step-by-step explanation:
