How Does the Central Limit Theorem Apply to Processing Times?

[Millacol88]

Homework Statement

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?

Homework Equations

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.

 

[Ray Vickson]

Homework Statement

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?

Homework Equations

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.

What do YOU think the Central Limit Theorem (not Central Limiting Theorem) says? Why do you think you can use it in this problem?