Let the random variable for the time taken to cook an egg be denoted as \(X\), where \(X \sim N(4.2, 0.6^2)\).

We need to find \(P(3.5 < X < 4.5)\).

Standardize the variable using the formula for the standard normal distribution: \(Z = \frac{X - \mu}{\sigma}\).

For \(X = 4.5\):

\(Z = \frac{4.5 - 4.2}{0.6} = \frac{0.3}{0.6} = 0.5\).

Thus, \(P(X < 4.5) = P(Z < 0.5) = 0.6915\).

For \(X = 3.5\):

\(Z = \frac{3.5 - 4.2}{0.6} = \frac{-0.7}{0.6} = -1.167\).

Thus, \(P(X < 3.5) = P(Z < -1.167) = 0.1216\).

Therefore, \(P(3.5 < X < 4.5) = P(X < 4.5) - P(X < 3.5) = 0.6915 - 0.1216 = 0.570\).