We need to find \(P(Y > 0)\). Since \(Y\) is normally distributed with mean \(\mu\) and standard deviation \(\sigma\), we can standardize \(Y\) to a standard normal variable \(Z\) using the formula:

\(Z = \frac{Y - \mu}{\sigma}\)

Thus, \(P(Y > 0) = P\left( Z > \frac{0 - \mu}{\sigma} \right)\).

Given \(4\sigma = 3\mu\), we can express \(\mu\) in terms of \(\sigma\):

\(\mu = \frac{4\sigma}{3}\)

Substitute \(\mu\) into the standardization formula:

\(P\left( Z > \frac{0 - \frac{4\sigma}{3}}{\sigma} \right) = P\left( Z > \frac{-4\sigma/3}{\sigma} \right) = P\left( Z > -\frac{4}{3} \right)\)

Using the standard normal distribution table, \(P(Z > -4/3) = 0.909\).