(i) To find the standard deviation \(\sigma\), we use the standard normal distribution formula:

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

Given \(P(X > 5.5) = 0.0465\), we find the corresponding \(z\)-value from the standard normal distribution table, which is approximately 1.68. Thus,

\(z = \frac{5.5 - 4.5}{\sigma} = 1.68\)

Solving for \(\sigma\), we get:

\(\sigma = \frac{1}{1.68} = 0.595\)

(ii) To find the probability that \(X\) lies between 3.8 and 4.8, we calculate the \(z\)-values for 3.8 and 4.8:

\(z_1 = \frac{3.8 - 4.5}{0.595} = -1.176\)

\(z_2 = \frac{4.8 - 4.5}{0.595} = 0.504\)

The probability is given by:

\(P(3.8 < X < 4.8) = \Phi(0.504) - (1 - \Phi(1.176))\)

Using the standard normal distribution table, \(\Phi(0.504) \approx 0.6929\) and \(\Phi(1.176) \approx 0.8802\), so:

\(P(3.8 < X < 4.8) = 0.6929 - (1 - 0.8802) = 0.573\)