Question:
Given that \(X\sim B(20,p)\) if \(E(X)=8\) then \(Var(X)\) is
Given that \(X\sim B(20,p)\) if \(E(X)=8\) then \(Var(X)\) is
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Use E(X) = np to find p, then Var(X) = npq.
Updated On: Nov 12, 2026
- \(\frac{8}{5}\)
- \(\frac{2}{5}\)
- \(\frac{24}{5}\)
- \(\frac{4}{5}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
For \(X\sim B(n,p)\), \(E(X)=np\) and \(Var(X)=npq\) with \(q=1-p\).
Step 2: Find p
\(20p=8\), so \(p=\dfrac{2}{5}\) and \(q=\dfrac{3}{5}\).
Step 3: Variance
\(Var(X)=20\times \dfrac{2}{5}\times \dfrac{3}{5}=\dfrac{24}{5}\).
Final Answer:
The variance is \(\dfrac{24}{5}\). \[ \boxed{\text{(C) }\dfrac{24}{5}} \]
For \(X\sim B(n,p)\), \(E(X)=np\) and \(Var(X)=npq\) with \(q=1-p\).
Step 2: Find p
\(20p=8\), so \(p=\dfrac{2}{5}\) and \(q=\dfrac{3}{5}\).
Step 3: Variance
\(Var(X)=20\times \dfrac{2}{5}\times \dfrac{3}{5}=\dfrac{24}{5}\).
Final Answer:
The variance is \(\dfrac{24}{5}\). \[ \boxed{\text{(C) }\dfrac{24}{5}} \]
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