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A binomial distribution has mean 4 and variance 2. Find the probability of exactly 2 successes.

1. 128/256
2. 219/256
3. 37/256
4. 28/256

Correct answer: 28/256

Solution

From np = 4 and npq = 2 we get q = 1/2, p = 1/2, n = 8; then P(X=2) = C(8,2)(1/2)⁸ = 28/256.

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