Q100 / 200 · Manipal (MET) 2010 · Mathematics

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

  • A
    16
  • B
    32
  • Correct answer
    C
    33
  • D
    None of these

Solution

Since, $(n+1) p=\frac{101}{3}$ is not an integer. Therefore, $p(X=r)$ is maximum when $r=\left[\frac{101}{3}\right]=33$

Hence, the correct answer is option: 'C'.

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