Let the random variable \(X\) represent the weight of the bags. \(X\) is normally distributed with mean \(\mu = 1.04\) kg and standard deviation \(\sigma = 0.06\) kg.

We need to find \(P(X > 1.11)\).

First, standardize the variable using the formula:

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

Substitute the values:

\(Z = \frac{1.11 - 1.04}{0.06} = 1.167\)

We need \(P(Z > 1.167)\).

Using standard normal distribution tables or a calculator, find \(P(Z > 1.167) = 1 - P(Z \leq 1.167)\).

From the tables, \(P(Z \leq 1.167) \approx 0.8784\).

Thus, \(P(Z > 1.167) = 1 - 0.8784 = 0.1216\).

Therefore, the probability that a randomly chosen bag weighs more than 1.11 kg is approximately \(0.122\).