Question

If x follows a binomial distribution with parameters $n=100$ and $p=1/3$, then $p(X=r)$ is maximum when r equals

• A. 16
• B. 32
• C. 33
• D. None of these

Hint:

If x follows a binomial distribution with parameters $n=100$ and $p=1/3$, then $p(X=r)$ is maximum when r equals

Answer 1

The Correct Option is C

Step 1: Concept
The mode of a binomial distribution occurs at the integer part of $(n+1)p$.
Step 2: Analysis
Calculate $(n+1)p = (100+1) \times 1/3 = 101/3$.
Step 3: Evaluation
$101/3 = 33.66...$.
Step 4: Conclusion
Since this is not an integer, the maximum probability occurs at $r = [33.66] = 33$.
Final Answer: (c)