(a)(i) To find the probability that Zak takes less than 30 minutes, we standardize the variable:

\(z = \frac{30 - 35.2}{4.7} = -1.106\)

Using the standard normal distribution table, \(P(z < -1.106) = 0.1345\).

The expected number of days in a year is \(0.1345 \times 52 = 6.99\), which rounds to 7 days.

(a)(ii) We know \(\Phi(t) = 0.648\) and \(z = 0.380\).

Standardizing, \(\frac{t - 35.2}{4.7} = 0.380\).

Solving for \(t\), we get \(t = 37.0\).

(b) We have two equations from the given probabilities:

\(\frac{7 - \mu}{\sigma} = -0.8\) and \(\frac{10 - \mu}{\sigma} = 0.44\).

Solving these equations simultaneously, we find \(\mu = 8.94\) and \(\sigma = 2.42\).