To find the standard deviation, we use the formula for the standard deviation of a sample:

\(\text{sd} = \sqrt{\frac{\Sigma(t - \bar{t})^2}{n}}\)

Given \(\Sigma(t - 2.5)^2 = 96.1\) and \(n = 250\), we first find the variance:

\(\text{variance} = \frac{96.1}{250} - (0.3)^2\)

where \(0.3\) is the coded mean difference \(2.8 - 2.5\).

\(\text{variance} = \frac{96.1}{250} - 0.09\)

\(\text{variance} = 0.3844 - 0.09 = 0.2944\)

Now, calculate the standard deviation:

\(\text{sd} = \sqrt{0.2944} = 0.543\)