$\sqrt{\frac{0.08(1-0.08)}{300}}=$

Step 1 ：We are given a standard deviation calculation for a binomial distribution. The formula for the standard deviation of a binomial distribution is \(\sqrt{np(1-p)}\), where n is the number of trials and p is the probability of success.

Step 2 ：In this case, n=300 and p=0.08. We can plug these values into the formula.

Step 3 ：Substituting the given values into the formula, we get \(\sqrt{\frac{0.08(1-0.08)}{300}}\)

Step 4 ：Solving the above expression, we get the standard deviation as 4.698936049788292

Step 5 ：Final Answer: \(\boxed{4.698936049788292}\)