An online computer system for submitting data is exponentially distributed with an expected response time of 2 seconds. If a team of 100 people all need to submit data, what is the probability of the whole process taking longer than 220 seconds?
I think L = 0.5 and I need to use F(x) = 1-e^(Lx), but I don't know where to put the 100 and 220. It does make me think about the CLT, but I don't think I can use it in this problem, because I don't have a variance value.
Hint:
The variance of an exponential distribution with mean $2$ (i.e. as you say a rate of $\frac12)$ is $4$, and the standard deviation is $2$
So the variance of the sum of $100$ such independent random variables is $400$ (standard deviation $20$) while the mean is $200$