#### 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.

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#### Step 1

1 of 4

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

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

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

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

\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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