To find the probability that a randomly chosen value of Y is negative, we need to standardize the variable. The standard normal variable Z is given by:

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

where \(\sigma = \frac{1}{2} \mu\). Therefore, the standardization becomes:

\(Z = \frac{0 - \mu}{\frac{1}{2} \mu} = \frac{-\mu}{\frac{1}{2} \mu} = -2\)

We need to find \(P(Y < 0) = P(Z < -2)\).

Using standard normal distribution tables, \(P(Z < -2) = 1 - P(Z < 2) = 1 - 0.9772 = 0.0228\).