JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-II

  • question_answer
    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

    Correct Answer: D

    Solution :

    [d] In binomial distribution, Mean = np = 10, variance = npq = 5 \[\therefore p=q=\frac{1}{2}\] Let x be the mode, then \[np+p>x>np-q\] \[\therefore 10+\frac{1}{2}>x>10-\frac{1}{2}\Rightarrow \frac{21}{2}>x>\frac{19}{2}\] \[\Rightarrow 9.5<x<10.5\Rightarrow x=10.\]


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