What expression defines the variance of a binomial distribution __________________?
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Answer: B. np (1 – p)
Explanation
The binomial distribution models the number of successes in n independent trials. Each trial has a constant probability of success denoted by the variable p. Mathematical derivation shows its variance equals the product npq where q is 1-p. Swiss mathematician Jacob Bernoulli pioneered the theory of binomial trials. The parameter n represents the total number of trials performed. It assumes binary outcomes commonly labeled as success and failure.
Quality inspectors use binomial variance to track defective items in batches. Medical researchers analyze success rates of clinical treatments using this formula. Polling organizations calculate sampling margins using binomial probability models. Option A represents the expected mean of a binomial distribution rather than variance. Option C uses division which contradicts the standard binomial variance formula. Option D uses an incorrect ratio of parameters for calculating variance.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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