Given that \(Y \sim N(\mu, \sigma^2)\) and \(2\sigma = 3\mu\), we need to find \(P(Y > 4\mu)\).

First, express \(\sigma\) in terms of \(\mu\):

\(2\sigma = 3\mu \Rightarrow \sigma = \frac{3\mu}{2}\)

Standardize the variable:

\(P(Y > 4\mu) = P\left( z > \frac{4\mu - \mu}{\sigma} \right) = P\left( z > \frac{3\mu}{\frac{3\mu}{2}} \right) = P(z > 2)\)

Using the standard normal distribution table, \(P(z > 2) = 1 - P(z \leq 2) = 1 - 0.9772 = 0.0228\).