设 $X_1, X_2, \cdots, X_n, \cdots$ 为独立同分布随机变量序列, 且均服从参数为 $\lambda(\lambda>1)$ 的指数分布, 记 $\Phi(x)$ 为标准正态分布函数, 则
A. $\lim _{n \rightarrow \infty} P\left\{\frac{\sum_{i=1}^n X_i-n \lambda}{\lambda \sqrt{n}} \leqslant x\right\}=\Phi(x)$
B. $\lim _{n \rightarrow \infty} P\left\{\frac{\sum_{i=1}^n X_i-n \lambda}{\sqrt{\lambda n}} \leqslant x\right\}=\Phi(x)$
C. $\lim _{n \rightarrow \infty} P\left\{\frac{\lambda \sum_{i=1}^n X_i-n}{\sqrt{n}} \leqslant x\right\}=\Phi(x)$
D. $\lim _{n \rightarrow \infty} P\left\{\frac{\sum_{i=1}^n X_i-\lambda}{\sqrt{n \lambda}} \leqslant x\right\}=\Phi(x)$