Let the random variable \(X\) represent the number of people whose birthday falls on a Monday. Since each day of the week is equally likely, the probability \(p\) that a person's birthday is on a Monday is \(\frac{1}{7}\).

We have \(n = 350\) people, so the expected number of people with a birthday on Monday is \(np = 350 \times \frac{1}{7} = 50\).

The variance is \(npq = 350 \times \frac{1}{7} \times \frac{6}{7} = 42.857\).

We use a normal approximation to the binomial distribution. Applying continuity correction, we find:

\(P(X \geq 47) = P\left( z > \frac{46.5 - 50}{\sqrt{42.857}} \right)\)

Calculating the z-score:

\(z = \frac{46.5 - 50}{\sqrt{42.857}} = -0.5346\)

Thus, \(P(z > -0.5346) = 0.704\).