The amounts of time that a cashier spends processing individual customers' orders are independent random variables with mean 2.5 minutes and standard deviation 2 minutes.
a) What is the approximate probability that it will take more than 4 hours to process orders of 100 people?
b)How many orders, at least, will be processed in 5 hours with probability 0.95?
c)Some orders are bigger and their mean processing time is 5 minutes with standard deviation of 3 minutes. If the probability of processing bigger orders is 0.2, what is the approximate probability that it will not take more than 5.5 hours to process orders of 100 customers?
The Attempt at a Solution
This seems like it would involve using the central limit theorem, since no information is given about the distribution except for mean and standard deviation. I'm unsure how to apply it though.