Given that the times follow a normal distribution \(N(\mu, \sigma^2)\) with \(\mu = 3\sigma\), we need to find \(P(t > 0.6\mu)\).

First, standardize the variable:

\(P(t > 0.6\mu) = P\left( z > \frac{0.6\mu - \mu}{\mu/3} \right)\)

Substitute \(\mu = 3\sigma\) into the equation:

\(P\left( z > \frac{0.6 \times 3\sigma - 3\sigma}{3\sigma/3} \right) = P(z > -1.2)\)

Using the standard normal distribution table, \(P(z > -1.2) = 0.885\).