CLT for a drifting interval

Let $X_{1},X_{2},…$ be a sequence of independent and identically distributed random variables with mean $4$ and variance $9$. If $T_{n}=\dfrac{1}{n}\sum_{i=1}^{n}X_{i}$, then $\lim_{n\to\infty}P\bigl(4\sqrt{n}-3<\sqrt{n}\,T_{n}<6+4\sqrt{n}\bigr)$ equals __________ (rounded off to two decimal places) [You may use $\Phi(2)=0.9772$, $\Phi(1.5)=0.9332$, $\Phi(1)=0.8413$]