Successive trials are conducted with replacement in which distribution:________________?
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Answer: B. Binomial distribution
Explanation
The binomial distribution models trials conducted with replacement to keep success probabilities constant. Replacing each sampled item ensures previous outcomes do not alter the composition of the population. This constant probability across trials satisfies the fundamental requirements of the binomial model. Sampling with replacement means selected items are returned to the population before the next draw. Sampling without replacement changes the remaining population proportions, typically requiring hypergeometric models. Binomial trials require a fixed number of independent attempts with binary success or failure outcomes.
Quality assurance inspectors use binomial models when testing large component batches with replacement. Survey researchers assume replacement conditions when drawing large samples from virtually infinite populations. Recognizing whether sampling uses replacement prevents errors in selecting probability distribution formulas. Hypergeometric distribution is used when trials are conducted without replacement from finite populations. Geometric distribution models the number of trials needed to achieve the first successful outcome. Option D is incorrect because binomial distribution correctly answers the replacement question.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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