Q. The mode of the binomial distribution for which mean and standard deviation are 10 and $\sqrt{5}\$respectively, is
A) 7
B) 8
C) 9
D) 10
Explanation
(d)
In binomial distribution, mean$= np = 10$, variance$= npq = 5$
$\therefore p = q = \frac{1}{2}$
Let $x$ be the mode, then
$np + p < x > np - q$
$\therefore\ 10 + \frac{1}{2} > x > 10 - \frac{1}{2}$
$\Rightarrow \ \frac{21}{2} > x > \frac{19}{2}\ \Rightarrow \ 9.5 < x < 10.5$
$\therefore\ x = 10$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.