First, calculate the probability that a bag weighs more than 2.6 kg:

\(P(X > 2.6) = \frac{134}{5000} = 0.0268\)

The probability that a bag weighs less than 2.6 kg is:

\(P(X < 2.6) = 1 - 0.0268 = 0.9732\)

Using the standard normal distribution, find the z-score corresponding to this probability:

\(\frac{2.6 - 2.55}{\sigma} = 1.93\)

Solving for \(\sigma\):

\(\sigma = \frac{2.6 - 2.55}{1.93} = 0.0259\)