Question:
Given $X\sim B(n,p)$, if $E(X)=4$ and $\text{Var}(X)=2.4$, then $n=$
Given $X\sim B(n,p)$, if $E(X)=4$ and $\text{Var}(X)=2.4$, then $n=$
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In binomial problems, use both mean and variance equations together to eliminate variables.
Updated On: Feb 18, 2026
- $20$
- $15$
- $5$
- $10$
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The Correct Option is D
Solution and Explanation
Step 1: Using formulas for binomial distribution.
For $X\sim B(n,p)$, \[ E(X)=np,\quad \text{Var}(X)=npq \]
Step 2: Substituting given values.
\[ np=4 \Rightarrow p=\frac{4}{n} \] \[ npq=2.4 \]
Step 3: Solving for $n$.
\[ 4\left(1-\frac{4}{n}\right)=2.4 \] \[ 4-\frac{16}{n}=2.4 \Rightarrow \frac{16}{n}=1.6 \Rightarrow n=10 \]
Step 4: Conclusion.
The value of $n$ is $10$.
For $X\sim B(n,p)$, \[ E(X)=np,\quad \text{Var}(X)=npq \]
Step 2: Substituting given values.
\[ np=4 \Rightarrow p=\frac{4}{n} \] \[ npq=2.4 \]
Step 3: Solving for $n$.
\[ 4\left(1-\frac{4}{n}\right)=2.4 \] \[ 4-\frac{16}{n}=2.4 \Rightarrow \frac{16}{n}=1.6 \Rightarrow n=10 \]
Step 4: Conclusion.
The value of $n$ is $10$.
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