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  4. The mode of the binomial distribution for which mean and standard deviation are 10 and √5 respectively, is

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Q. The mode of the binomial distribution for which mean and standard deviation are 10 and $ \sqrt{5} $ respectively, is

Bihar CECEBihar CECE 2014

Solution:

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