First, calculate the probability of a bag weighing more than 2.1 kg:

\(P(x > 2.1) = \frac{253}{8000} = 0.031625\)

Thus, the probability of a bag weighing less than 2.1 kg is:

\(P(x < 2.1) = 1 - 0.031625 = 0.968375\)

This corresponds to the cumulative distribution function \(\Phi(z)\), so:

\(\Phi(z) = 0.968375\)

Using standard normal distribution tables, find \(z\) such that \(\Phi(z) = 0.968375\). This gives:

\(z = 1.857 \text{ or } 1.858 \text{ or } 1.859\)

Using the z-score formula:

\(z = \frac{2.1 - 2.04}{\sigma}\)

Substitute \(z = 1.857\) (or similar values) to solve for \(\sigma\):

\(1.857 = \frac{2.1 - 2.04}{\sigma}\)

\(\sigma = \frac{0.06}{1.857} \approx 0.0323\)