To find the probability that \(X\) lies between 25 and 30, we standardize the values using the formula for the standard normal variable \(Z\):

\(z = \frac{x - \mu}{\sigma}\)

where \(\mu = 28.3\) and \(\sigma = \sqrt{4.5}\).

First, calculate \(z_1\) for \(x = 30\):

\(z_1 = \frac{30 - 28.3}{\sqrt{4.5}} = 0.8014\)

Next, calculate \(z_2\) for \(x = 25\):

\(z_2 = \frac{25 - 28.3}{\sqrt{4.5}} = -1.5556\)

The probability that \(X\) lies between 25 and 30 is given by:

\(\Phi(z_1) - \Phi(z_2) = \Phi(0.8014) - (1 - \Phi(-1.5556))\)

Using standard normal distribution tables or a calculator, we find:

\(\Phi(0.8014) = 0.7884\)

\(\Phi(-1.5556) = 0.0599\)

Thus, the probability is:

\(0.7884 + 0.9401 - 1 = 0.729\)