Suppose $64$ students are taking an exam. The exam has $16$ questions in multiple choice format. Students must fill an oval for every one of the $16$ questions. They can't revise their answers. The time taken for a students to answer a question is exponentially distributed with mean $8$ minutes. So $f(t) = \frac{1}{8}e^{-t/8}$. The times for answering questions are independent. Using the normal approximation calculate the probability that the average time taken by the students is more than $132$ minutes.
So we want to find $P[T_1+T_2 + \cdots + T_{64} > 132(64)]$. What would be the distribution of a sum of exponential random variables? Would it be a gamma distribution? If we let $S = T_{1} + T_{2} + \cdots + T_{64}$, then $P[S > 132(64)] = 1-P[S \leq 132(64)]$.