Question

Assume a binomial probability distribution with n = 50 and π = .25. Compute the following: a. The mean and standard deviation of the random variable. b. The probability that X is 15 or more. c. The probability that X is 10 or less.

Solution

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The binomial distribution has n=50n=50 and π=0.25\pi=0.25.

a. Mean of the distribution μ\textbf{a. Mean of the distribution $\mu$}

μ=nπ=50×0.25=12.5\begin{align*} \mu&=n\pi\\ &=50 \times 0.25\\ &=12.5\\ \end{align*}

  Standard deviation of the distribution σ\textbf{ \ Standard deviation of the distribution $\sigma$}

σ=nπ(1π)=50×0.25×(10.25)=9.375=3.062\begin{align*} \sigma&=\sqrt{n\pi(1-\pi)}\\ &=\sqrt{50\times 0.25 \times (1-0.25)}\\ &=\sqrt{9.375}\\ &=3.062\\ \end{align*}

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