JEE Main & Advanced Sample Paper JEE Main - Mock Test - 6

  • question_answer
    For the binomial distribution \[{{(p+q)}^{n}}\], whose mean is 20 and variance is 16, pair (n, p) is

    A) \[\left( 100,\frac{1}{5} \right)\]

    B) \[\left( 100,\frac{2}{5} \right)\]

    C) \[\left( 50,\frac{1}{5} \right)\]      

    D) \[\left( 50,\frac{2}{5} \right)\]

    Correct Answer: A

    Solution :

    [a] : For binomial distribution mean \[=np=20\]     ...(i) variance = npq =16                               (ii) \[20q=16\]                                (from (i) and (ii)) \[\Rightarrow \]\[q=\frac{4}{5}\]\[\Rightarrow \]\[1-p=\frac{4}{5}\]\[\Rightarrow \]\[p=\frac{1}{5}\] Now,\[n\times \frac{1}{5}=20\Rightarrow n=100\] \[\therefore \]\[(n,p)=\left( 100,\frac{1}{5} \right)\] 

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