(a) To find the probability that Pia takes longer than 11.3 minutes, we use the standard normal distribution. First, we standardize the variable:

\(P(X > 11.3) = P\left( Z > \frac{11.3 - 10.1}{1.3} \right) = P(Z > 0.9231)\)

Using the standard normal distribution table, \(P(Z > 0.9231) = 1 - P(Z < 0.9231) = 1 - 0.822\)

Thus, \(P(X > 11.3) = 0.178\).

(c) To find the number of days Pia takes between 8.9 and 11.3 minutes, we calculate:

\(P(8.9 < X < 11.3) = 1 - 2 \times P(X > 11.3)\)

\(= 2 \times (0.5 - 0.178) = 0.644\)

The expected number of days is \(90 \times 0.644 = 57.96\), which rounds to 57 days.