To find the probability that \(X < 29.4\), we first standardize the variable using the formula for the standard normal distribution:

\(P(X < 29.4) = P\left(Z < \frac{29.4 - 31.4}{\sqrt{3.6}}\right)\)

Calculating the standardized value:

\(\frac{29.4 - 31.4}{\sqrt{3.6}} = -1.0541\)

Thus, \(P(X < 29.4) = P(Z < -1.0541)\).

Using the standard normal distribution table, we find:

\(P(Z < -1.0541) = 1 - 0.8540 = 0.146\)

Therefore, the probability that a randomly chosen value of \(X\) is less than 29.4 is 0.146.