(a) To find the probability that Raj runs for more than 43.2 minutes, we use the standard normal distribution. First, we calculate the z-score:

\(z = \frac{43.2 - 41.2}{3.6} = 0.5556\)

We need to find \(P(Z > 0.5556)\). Using the standard normal distribution table, \(\Phi(0.5556) = 0.7108\).

Therefore, \(P(Z > 0.5556) = 1 - 0.7108 = 0.2892\).

So, the probability that Raj runs for more than 43.2 minutes is approximately 0.289.

(b) To find the number of days Raj runs for less than 43.2 minutes, we calculate:

\(P(X < 43.2) = 1 - P(X > 43.2) = 1 - 0.2892 = 0.7108\).

Multiply this probability by the number of days in a year:

\(0.7108 \times 365 = 259.4\).

Therefore, the estimated number of days is approximately 259 or 260.