In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

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In this question we are dealing with counting the number of blemishes in a fixed length of material (100 feet). The key is to choose a distribution that models the count of rare, independent events occurring in a continuous interval or space.
Option 1: binomial distribution. The binomial model requires a predetermined number of independent trials and a constant probability of success in each trial. Here we are not counting successes over a fixed number of trials; instead we are counting blemishes along a length, which makes the binomial form less natural unless we explicitly redefine trials. Therefore this option is not the best fit for a per-length count of defects.
Option 2: Poisson distribution. The Poisson model is designed for counting the number of events (blemishes) that occur in a fixed interval (100 feet) when events are rare and occur independently, and the average rate is stable across intervals. This aligns well with the described scenario, making Poisson the most appropriate choice.
Option 3: normal distribution. While the normal distribution can approximate Poisson counts when the mean count is large, it is not the most exact or fundamental model for rare-event counts in a fixed interval. Relying on normal approximation sacrifices discreteness and can misrepresent probabilities at low counts, so it’s not the primary model here.
Option 4: uniform distribution. A uniform distribution would imply that all counts within a range are equally likely, which is inconsistent with the natural idea of counts clustering around a mean and diminishing toward extremes. This makes it an unsuitable choice for blemish counts in a material length.

In the textile industry, a manufacturer is interested in the number of blemishes or flaws occurring in each 100 feet of material. The probability distribution that has the greatest chance of applying to this situation is the

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