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If $E(X) = 6$ and $\text{Var}(X) = 4.2$ for $X \sim B(n, p)$, then $n$ and $p$ are:
A$n = 20, p = 0.3$
B$n = 10, p = 0.6$
C$n = 30, p = 0.2$
D$n = 12, p = 0.5$
Answer & Solution
Correct answer: A. $n = 20, p = 0.3$
$q = \text{Var}/E = 4.2/6 = 0.7$ ⇒ $p = 0.3$. Then $np = 6$ ⇒ $n = 6/0.3 = 20$.
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