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For a binomial distribution the mean is 4 and the variance is 3. What is the probability of obtaining exactly six successes?
- 16C6 * (1/4)¹⁰ * (3/4)⁶
- 16C6 * (1/4)⁶ * (3/4)¹⁰
- 12C6 * (1/4)¹⁰ * (3/4)⁶
- 12C6 * (1/4)⁶ * (3/4)¹⁰
Correct answer: 16C6 * (1/4)⁶ * (3/4)¹⁰
Solution
From np = 4 and npq = 3, q = 3/4, p = 1/4 and n = 16, so P(X=6) = 16C6 (1/4)⁶ (3/4)¹⁰.
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