Let the mean be \(\mu\) and the standard deviation be \(\sigma\).

For the time less than 36 minutes, 23% corresponds to a \(z\)-score of approximately \(-0.739\). Thus,

\(z_1 = \frac{36 - \mu}{\sigma} = -0.739\)

For the time greater than 54 minutes, 10% corresponds to a \(z\)-score of approximately \(1.282\). Thus,

\(z_2 = \frac{54 - \mu}{\sigma} = 1.282\)

We have two equations:

1. \(\frac{36 - \mu}{\sigma} = -0.739\)
2. \(\frac{54 - \mu}{\sigma} = 1.282\)

Solving these equations simultaneously, we find:

\(\mu = 42.6\)

\(\sigma = 8.91\)