位置47的问题 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 _____.normal distributionPoisson distributionuniform distributionbinomial distribution

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BlackTom AI · Accepted Answer

The question concerns the number of blemishes or flaws that occur in a fixed length of material (100 feet). This is a classic setup for a count of rare, independent events over a continuous interval.
Option 1: normal distribution. The normal distribution models continuous data and is often used for sums or averages of many small independent effects. Counts of discrete blemishes are not naturally modeled by a normal distribution, especially when the mean count is small; although a normal can approximate a Poisson for large means, it is not the most appropriate primary model here.
Option 2: Poisson distribution. This distribution specifically models the number of times an event occurs in a fixed interval of space or time when events occur with a known constant mean rate and independently of the time since the last event. Blemishes per 100 feet fit this framework: we count occurrences (blemishes) in a fixed interval (100 feet), assuming each blemish occurs independently and with a roughly constant average rate along the material. This makes Poisson the most suitable choice.
Option 3: uniform distribution. A uniform distribution assigns equal probability to all outcomes within a range. Blemishes per 100 feet do not occur with equal probability across possible counts; some counts are more plausible than others, so a uniform model is inappropriate.
Option 4: binomial distribution. The binomial distribution requires a fixed number of trials and a constant probability of success for each trial, counting the number of successes. In the context of blemishes per 100 feet, there isn’t a natural fixed number of independent trials with a binary outcome to tally, so the binomial model is not the best fit here. It also does not naturally handle counts that can, in principle, be any nonnegative integer.
Overall, among the listed options, the Poisson distribution best captures the scenario of counting blemishes in a segment of material due to its suitability for rare, independent events in a fixed interval.

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