The probability that a bag weighs more than 1.10 kg is given by:

\(P(X > 1.1) = \frac{72}{2000} = 0.036\)

Using the standard normal distribution, this corresponds to a \(z\)-value of approximately \(z = 1.798\).

We use the standardization formula:

\(z = \frac{X - \mu}{\sigma}\)

Substituting the known values:

\(1.798 = \frac{1.1 - 1.04}{\sigma}\)

\(1.798 = \frac{0.06}{\sigma}\)

Solving for \(\sigma\):

\(\sigma = \frac{0.06}{1.798} \approx 0.0334\)