I have problem with this example:
They didn't rest for a minute today at the box office, someone had been there all day. The time required for customer check-in has an exponential distribution. In eight hours they handled exactly 160 customers. How much time at the cash register would be enough for check-in half of the customers?
I think, that the answer is 4 hours, because it doesnt matter what distribution has one customer when they are all independent. But it was said to me that it is incorrect. Can someone explain it to me? How should I calculate it then? I know that the variance is +-3 minutes, but that is for all the customers together. Why it is not half the time for half the customers?