(a) We know that \(P(X < 16) = 0.1\). Using the standard normal distribution, we find the z-value corresponding to 0.1, which is approximately \(-1.282\).

Using the standardization formula:

\(\frac{16 - 28}{\sigma} = -1.282\)

Solving for \(\sigma\):

\(\sigma = \frac{12}{1.282} \approx 9.36\)

(c) We need to find \(P(-1.3 < Z < 1.3)\).

Using the standard normal distribution table, \(\Phi(1.3) \approx 0.9032\).

Thus, \(P(-1.3 < Z < 1.3) = 2 \times 0.9032 - 1 = 0.8064\).

In 365 days, the expected number of days is:

\(0.8064 \times 365 \approx 294.336\)

Therefore, the expected number of days is 294 or 295.