To find the probability that \(X < -2.4\), we first standardize the variable using the formula for the standard normal distribution:

\(P(X < -2.4) = P\left( Z < \frac{-2.4 - 1.5}{3.2} \right)\)

Calculating the standardized value:

\(\frac{-2.4 - 1.5}{3.2} = \frac{-3.9}{3.2} = -1.219\)

Now, we find \(P(Z < -1.219)\) using the standard normal distribution table or a calculator:

\(P(Z < -1.219) = 1 - P(Z < 1.219)\)

From the standard normal distribution table, \(P(Z < 1.219) \approx 0.8886\).

Therefore, \(P(Z < -1.219) = 1 - 0.8886 = 0.1114\).

Rounding to three decimal places, the probability is \(0.111\).