$\begin{aligned} \sigma_{p} & =\sqrt{\frac{p(1-p)}{n}} \\ & =\sqrt{\frac{0.08(1-0.08)}{256}}\end{aligned}$

Step 1 ：The question is asking for the standard deviation of a binomial distribution, denoted as \(\sigma_{p}\). The formula for the standard deviation of a binomial distribution is \(\sqrt{\frac{p(1-p)}{n}}\), where p is the probability of success and n is the number of trials.

Step 2 ：In this case, p = 0.08 and n = 256. We need to substitute these values into the formula.

Step 3 ：So, \(\sigma_{p} = \sqrt{\frac{0.08(1-0.08)}{256}}\)

Step 4 ：After calculating, we get \(\sigma_{p} = 0.01695582495781317\)

Step 5 ：So, the final answer is \(\boxed{0.01695582495781317}\)