Q113 / 170 · Manipal (MET) 2019 · 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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