Question:
In a Binomial distribution with \(n=10\) and \(p=0.4\), find the variance.
In a Binomial distribution with \(n=10\) and \(p=0.4\), find the variance.
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For a binomial distribution:
Mean \(= np\)
Variance \(= npq\)
Standard deviation \(=\sqrt{npq}\).
Updated On: Apr 20, 2026
- \(2.0\)
- \(2.4\)
- \(4.0\)
- \(3.2\)
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The Correct Option is B
Solution and Explanation
Concept:
For a binomial distribution,
\[
\text{Variance} = npq
\]
where
• \(n\) = number of trials
• \(p\) = probability of success
• \(q = 1-p\)
Step 1: Find the value of \(q\). \[ q=1-p \] \[ q=1-0.4=0.6 \]
Step 2: Substitute into the variance formula. \[ \text{Variance}=npq \] \[ =10 \times 0.4 \times 0.6 \] \[ =2.4 \] Thus the variance is \[ \boxed{2.4} \]
• \(n\) = number of trials
• \(p\) = probability of success
• \(q = 1-p\)
Step 1: Find the value of \(q\). \[ q=1-p \] \[ q=1-0.4=0.6 \]
Step 2: Substitute into the variance formula. \[ \text{Variance}=npq \] \[ =10 \times 0.4 \times 0.6 \] \[ =2.4 \] Thus the variance is \[ \boxed{2.4} \]
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