A given binomial distribution has mean-4 and variance-2. What is the probability of success? Explain your answer.

Question

A given binomial distribution has mean-4 and variance-2. What is the probability of success? Explain your answer.

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Everleigh 2 weeks 2021-09-09T09:50:22+00:00 1 Answer 0

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    2021-09-09T09:52:02+00:00

    Answer: 0.5

    Step-by-step explanation:

    We know that the mean and variance of a binomial distribution with probability of success p is given by :-

    \text{Mean}:\mu=np\\\\\text{Variance}:\sigma^2=np(1-p), where n is the total number of trials .

    Given : A given binomial distribution has

    \text{Mean}:\mu=np=4.......(1)\\\\\text{Variance}:\sigma^2=np(1-p)=2............(2)

    Now we substitute , the value of np from (1) in (2), we get

    4(1-p)=2\\\\\Rightarrow\ 1-p=\dfrac{2}{4}\\\\\Rightarrow\ p=1-\dfrac{1}{2}\\\\\Rightarrow\ p=\dfrac{1}{2}=0.5

    Hence, the probability of success (p) = 0.5

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