Empirical Frequency Accuracy via the CLT

A biased die shows a six with probability $p = 1/3$. You roll it $n = 900$ times independently and record $\hat{p} = (\text{number of sixes})/n$.

(a) State what the Law of Large Numbers guarantees about $\hat{p}$ as $n \to \infty$.

(b) Using the CLT, approximate $P(|\hat{p} - 1/3| < 0.02)$.

You may use $\Phi(1.27) \approx 0.8980$.