Call Center Overflow via Poisson CLT

A call center receives calls according to a Poisson process with rate $\lambda = 4$ calls per minute. The center operates for an $8$-hour shift ($480$ minutes). The center can handle at most $2000$ calls per shift before service quality degrades.

Using a suitable normal approximation, estimate the probability that the total number of calls in a single shift exceeds $2000$.

You may use the following: $\Phi(1.83) \approx 0.9664$.