Let \(z_1\) and \(z_2\) be the standard normal variables corresponding to the given percentages.

For 20% of students having times less than 14.5 minutes, \(z_1 = \frac{14.5 - \mu}{\sigma} = -0.842\).

For 67% of students having times greater than 18.5 minutes, 33% have times less than 18.5 minutes, so \(z_2 = \frac{18.5 - \mu}{\sigma} = -0.44\).

We have the equations:

1. \(\frac{14.5 - \mu}{\sigma} = -0.842\)
2. \(\frac{18.5 - \mu}{\sigma} = -0.44\)

Solving these equations simultaneously, we find:

\(\mu = 22.9\)

\(\sigma = 9.95\)