Question

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

Answer 1

Answer: (D)

In a binomial distribution, mean, $np=10$ and variance, $npq=5$ $\therefore$ $10\times q=5\Rightarrow q=\frac{1}{2}$ $\Rightarrow$ $p=1-q=1-\frac{1}{2}=\frac{1}{2}$ Let x be the mode. Then, $np+q>x>np-q$ $\Rightarrow$ $10+\frac{1}{2}>x>10-\frac{1}{2}$ $\Rightarrow$ $\frac{21}{2}>x>\frac{19}{2}\Rightarrow 9.5<x<1.05$ Hence, option (d) is correct.