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Mean and variance of a binomial distribution are 4 and 2 respectively. The probability of **exactly 2** successes is:
A$28/256$
B$128/256$
C$219/256$
D$37/256$
Answer & Solution
Correct answer: A. $28/256$
$np = 4, npq = 2$ ⇒ $q = 1/2, p = 1/2, n = 8$. $P(X = 2) = {}^8C_2 (1/2)^2 (1/2)^6 = 28 \cdot (1/256) = 28/256$.
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