Discussion
The standard deviation of a binomial distribution is ............
Answer: C
The standard deviation of a binomial distribution is \(\sqrt{npq}\).
For a binomial distribution with n trials, probability of success p and probability of failure q = 1 - p, the mean and variance are:
\[ \begin{aligned} \mu &= np \\ \sigma^{2} &= npq \\ \sigma &= \sqrt{npq} \end{aligned} \]
So np is the mean, not the standard deviation, and npq is the variance; the standard deviation is its square root. The expression \(np^{2}q^{2}\) has no role in the binomial distribution. For example, with n = 100 and p = q = 0.5, the mean is 50, the variance 25 and the standard deviation 5.
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