Allied & ICAR Exam Bank • ALLIED_2747 MCQ • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Poisson, normal and binomial distributions

Question Statement:

In a binomial distribution $B(n, p)$, the variance is maximized when $p$ equals:

Options:

  • (A) $0.5$
  • (B) $1.0$
  • (C) $0.0$
  • (D) $0.25$

Answer Key:

A

Step-by-Step Solution & Explanation

$\text{Var} = n p (1 - p)$. The quadratic $p(1 - p)$ reaches its maximum of $0.25$ at $p = 0.5$.
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