We need to find the probability that a cartridge contains less than 28.9 ml of ink. Let the random variable representing the volume of ink be normally distributed as \(X \sim N(30, 1.5^2)\).

We standardize the variable to find \(P(X < 28.9)\):

\(P(X < 28.9) = P\left( Z < \frac{28.9 - 30}{1.5} \right) = P(Z < -0.733)\)

Using the standard normal distribution table, \(P(Z < -0.733) = 1 - 0.7682 = 0.2318\).

The expected number of cartridges per month that contain less than 28.9 ml is:

\(0.2318 \times 8 = 1.85\)

Rounding to the nearest whole number, we get 2 cartridges.