Sum of Uniform Random Variables Exceeding a Threshold

Let $U_1, U_2, \ldots, U_{60}$ be independent $\mathrm{Uniform}(0,1)$ random variables, and define $S = \sum_{i=1}^{60} U_i$.

Using the CLT, approximate $P(S > 35)$.

You may use $\Phi(2.24) \approx 0.9875$.