Q. If the mean and standard deviation of a binomial distribution are 12 and 2 respectively, then value of its parameter $p$ is
A) $1/2$
B) 1/3
C) 2/3
D) $1/4$
Explanation
(c)
Given that, $np = 12$ …(i)
and $\sqrt{npq} = 2\ \Rightarrow npq = 4$ ...(ii)
From Eqs. (i) and (ii), we get
$12 \times q = 4\ \Rightarrow q = \frac{1}{3}$
and we know that,
$p + q = 1\ \Rightarrow p = 1 - \frac{1}{3} = \frac{2}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.