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Poisson Distribution Analysis

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A textile manufacturer estimates that it produces bolts of cloth with flaws following a Poisson distribution that has an average of one flaw per 200 feet of cloth.

a. Find the probability that a given 200-foot length of cloth will have no flaws.
b. What is the probability that there will be at least one flaw within a given 200 foot length of cloth?
c. What is the probability that there will be two or fewer flaws in a given 300 foot length of cloth?

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This solution provides a detailed, step-by-step explanation of the given probability problem.

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A textile manufacturer estimates that it produces bolts of cloth with flaws following a Poisson distribution that has an average of one flaw per 200 feet of cloth.

a. Find the probability that a given 200-foot length of cloth will have no flaws

Solution. Let X be the number of flaws that a given 200-foot length of cloth will ...

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Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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