Central Limiting Theorem?

  • Thread starter Millacol88
  • Start date
  • #1
86
0

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.
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

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?
 
Last edited:

Related Threads on Central Limiting Theorem?

  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
9
Views
1K
Replies
2
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
21
Views
2K
Replies
2
Views
1K
Replies
1
Views
1K
Top